Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2023-24
Module Leader
Lecturers
Prof Andrew Gee, Prof Graham Treece
Timing and Structure
Lent term. 10 flipped classroom interactive seminars and 6 traditional lectures. Lectures (but not seminars) will be recorded.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6 lectures, Prof Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data and analyse some basic geometric properties of the surfaces. Finally, they use Vulkan to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in a Vulkan framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 30/05/2023 15:22
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2024-25
Module Leader
Lecturers
Prof Andrew Gee, Prof Graham Treece
Timing and Structure
Lent term. 10 flipped classroom interactive seminars and 6 traditional lectures. Lectures (but not seminars) will be recorded.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6 lectures, Prof Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data and analyse some basic geometric properties of the surfaces. Finally, they use Vulkan to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in a Vulkan framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 31/05/2024 09:55
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2018-19
Module Leader
Lecturers
Dr A Gee, Dr G Treece and Prof R Prager
Lab Leader
Dr G Treece
Timing and Structure
Lent term. 16 lectures.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the popular imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using advanced computer graphic techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (5L, Prof Richard Prager)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6L, Dr Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (5L, Dr Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data, writing algorithms to calculate the volumes enclosed by the surfaces. Finally, they use OpenGL to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in an OpenGL framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Group G Courses for references to this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 16/05/2018 13:46
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2022-23
Module Leader
Lecturers
Prof Andrew Gee and Dr Flavia Mancini
Timing and Structure
Lent term. 10 flipped classroom interactive seminars and 6 traditional lectures. Lectures (but not seminars) will be recorded.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6 lectures, Dr Flavia Mancini)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data, writing algorithms to calculate the volumes enclosed by the surfaces. Finally, they use OpenGL to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in an OpenGL framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 18/07/2022 17:47
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2021-22
Module Leader
Lecturers
Dr Andrew Gee & Dr Graham Treece
Lab Leader
Dr Graham Treece
Timing and Structure
Lent term. 16 lectures.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (5L, Dr Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6L, Dr Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (5L, Dr Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data, writing algorithms to calculate the volumes enclosed by the surfaces. Finally, they use OpenGL to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in an OpenGL framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 20/05/2021 07:37
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2025-26
Module Leader
Lecturers
Prof Andrew Gee, Prof Graham Treece
Timing and Structure
Lent term. 10 flipped classroom interactive seminars and 6 traditional lectures. Lectures (but not seminars) will be recorded.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6 lectures, Prof Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data and analyse some basic geometric properties of the surfaces. Finally, they use Vulkan to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in a Vulkan framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 04/06/2025 13:22
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2020-21
Module Leader
Lecturers
Dr Andrew Gee & Dr Graham Treece
Lab Leader
Dr Graham Treece
Timing and Structure
Lent term. 16 lectures.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (5L, Dr Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6L, Dr Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (5L, Dr Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data, writing algorithms to calculate the volumes enclosed by the surfaces. Finally, they use OpenGL to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in an OpenGL framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 28/08/2020 11:09
Engineering Tripos Part IIA, 3F4: Data Transmission, 2018-19
Module Leader
Lecturers
Dr R Venkataramanan, Prof. Ioannis Kontoyiannis
Lab Leader
Timing and Structure
Lent term. 16 lectures
Prerequisites
Knowledge of 3F1 assumed.
Aims
The aims of the course are to:
- Cover a range of topics which are important in modern communication systems.
- Extend the basic material covered in the Engineering Part IB Communications course to deal with data transmission over baseband (low frequency) channels as well bandpass (higher frequency) channels.
- Analyse the effects of noise in some detail.
- Understand the technique of convolutional coding to protect information transmitted over noisy channels.
- To understand basic congestion control protocols (TCP/IP), and routing algorithms used in the Internet.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand the different components of a communication network, in particular the role of the physical layer versus the network layer.
- Be able to represent waveforms as vectors in a signal space.
- Appreciate that pulses may be shaped to control the bandwidth of a signal and reduce inter-symbol interference, and be aware of the limits on transmission rate if ISI is to be avoided.
- Be able to describe and analyse demodulation of digital bandpass modulated signals in noise.
- Calculate the probability of error of various modulation schemes as a function of the signal-to-noise-ratio.
- Appreciate how equalisation can correct for undesirable channel characteristics and be able to design simple equalisers.
- Understand the principles of Orthogonal Frequency Division Multiplexing for communication over multi-path wideband channels
- Understand the need for coding, i.e., adding redundancy to control the effects of transmission errors.
- Understand the principles of convolutional coding, and be able to design a Viterbi decoder for convolutional codes.
- Understand the operation of congestion control protocols (TCP/IP) and routing algorithms used in the internet
Content
Fundamentals of Modulation and Demodulation (7L)
- Introduction: The overall commuication network and the roles of the physical layer and the network layer
- Signal Space: representing waveforms as elements a vector space
- Baseband modulation: Desirable properties of the pulse for PAM; Nyquist criterion for no inter-symbol interference; Eye-diagrams
- Modelling the noise as a Gaussian random process. Additive White Gaussian Noise (AWGN)
- Optimal demodulation and detection at the receiver in the presence of AWGN: Matched filter demodulator, optimal detection using the maximum-a-posteriori probability (MAP) rule
- Passband modulation: QAM, M-ary FSK (Orthogonal signalling)
- Performance analysis of modulation schemes (PAM, QAM, Orthogonal signaling etc.): probability of detection error and bandwidth efficiency
Advanced Topics in PHY-layer (3L)
- Brief discussion of coded modulation
- Equalisation techniques to deal with inter-symbol interference: ZF and MMSE equalizers
- Orthogonal Frequency Division Multiplexing (OFDM)
Channel Coding (3L)
- Introduction to error correction and linear codes
- Convolutional codes: State Diagram and Trellis representations, Viterbi decoding algorithm
- Distance properties of convolutional codes using the transfer function derived from state diagram; free-distance of convolutional codes.
Network Algorithms (3L)
- Congestion control in the Internet: window-based congestion control: TCP-Reno; slow-start, congestion avoidance
- Routing algorithms in the Internet: Djikstra's algorithm, Bellman-Ford and the similarities to the Viterbi algorithm
Further notes
The syllabus for this module was updated (with significant changes) in 2017-18. A list of relevant past Tripos questions is available on Moodle.
Coursework
Digital transmission systems
Learning objectives:
- To investigate, using a hardware simulation of baseband transmission channels, the phenomenon of inter-symbol interference, and to measure bit error rate (BER) due to noise
- To use the eye diagram as a diagnostic tool, and to understand its limitations.
- To compare the measured dependence of BER on signal-to-noise Ratio (SNR) with theoretical predictions, and explain the differences by considering how the assumptions made in the theoretical analysis compare with the real situation.
Practical information:
- Sessions will take place in EIETL, during week(s) [xxx].
- This activity involves preliminary work-- reading the lab handout ([estimated duration: 1 hour]).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
For Physical-layer communications (first 13L):
- B. Rimoldi, Principles of Digital Communication: A Top-Down Approach, Cambridge University Press, 2016]
- R. Gallager, Principles of Digital Communication, Cambridge University Press, 2008
- U. Madhow, Fundamentals of Digital Communication, Cambridge University Press, 2008
For network algorithms (last 3L):
- R. Srikant and L. Ying, Communication Networks, Cambridge University Press, 2014.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 12/12/2018 17:46
Engineering Tripos Part IIA, 3F4: Data Transmission, 2017-18
Module Leader
Lecturers
Dr R Venkataramanan, Prof. Ioannis Kontoyiannis
Lab Leader
Timing and Structure
Lent term. 16 lectures
Prerequisites
Knowledge of 3F1 assumed.
Aims
The aims of the course are to:
- Cover a range of topics which are important in modern communication systems.
- Extend the basic material covered in the Engineering Part IB Communications course to deal with data transmission over baseband (low frequency) channels as well bandpass (higher frequency) channels.
- Analyse the effects of noise in some detail.
- Understand the technique of convolutional coding to protect information transmitted over noisy channels.
- To understand basic congestion control protocols (TCP/IP), and routing algorithms used in the Internet.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand the different components of a communication network, in particular the role of the physical layer versus the network layer.
- Be able to represent waveforms as vectors in a signal space.
- Appreciate that pulses may be shaped to control the bandwidth of a signal and reduce inter-symbol interference, and be aware of the limits on transmission rate if ISI is to be avoided.
- Be able to describe and analyse demodulation of digital bandpass modulated signals in noise.
- Calculate the probability of error of various modulation schemes as a function of the signal-to-noise-ratio.
- Appreciate how equalisation can correct for undesirable channel characteristics and be able to design simple equalisers.
- Understand the principles of Orthogonal Frequency Division Multiplexing for communication over multi-path wideband channels
- Understand the need for coding, i.e., adding redundancy to control the effects of transmission errors.
- Understand the principles of convolutional coding, and be able to design a Viterbi decoder for convolutional codes.
- Understand the operation of congestion control protocols (TCP/IP) and routing algorithms used in the internet
Content
Fundamentals of Modulation and Demodulation (7L)
- Introduction: The overall commuication network and the roles of the physical layer and the network layer
- Signal Space: representing waveforms as elements a vector space
- Baseband modulation: Desirable properties of the pulse for PAM; Nyquist criterion for no inter-symbol interference; Eye-diagrams
- Modelling the noise as a Gaussian random process. Additive White Gaussian Noise (AWGN)
- Optimal demodulation and detection at the receiver in the presence of AWGN: Matched filter demodulator, optimal detection using the maximum-a-posteriori probability (MAP) rule
- Passband modulation: QAM, M-ary FSK (Orthogonal signalling)
- Performance analysis of modulation schemes (PAM, QAM, Orthogonal signaling etc.): probability of detection error and bandwidth efficiency
Advanced Topics in PHY-layer (3L)
- Brief discussion of coded modulation
- Equalisation techniques to deal with inter-symbol interference: ZF and MMSE equalizers
- Orthogonal Frequency Division Multiplexing (OFDM)
Channel Coding (3L)
- Introduction to error correction and linear codes
- Convolutional codes: State Diagram and Trellis representations, Viterbi decoding algorithm
- Distance properties of convolutional codes using the transfer function derived from state diagram; free-distance of convolutional codes.
Network Algorithms (3L)
- Congestion control in the Internet: window-based congestion control: TCP-Reno; slow-start, congestion avoidance
- Routing algorithms in the Internet: Djikstra's algorithm, Bellman-Ford and the similarities to the Viterbi algorithm
Further notes
The syllabus for this module has been revised for 2017-18, and therefore the lecture notes, examples papers etc. will be different from previous years. A list of relevant past Tripos questions will be provided towards the end of the module.
Coursework
Digital transmission systems
Learning objectives:
- To investigate, using a hardware simulation of baseband transmission channels, the phenomenon of inter-symbol interference, and to measure bit error rate (BER) due to noise
- To use the eye diagram as a diagnostic tool, and to understand its limitations.
- To compare the measured dependence of BER on signal-to-noise Ratio (SNR) with theoretical predictions, and explain the differences by considering how the assumptions made in the theoretical analysis compare with the real situation.
Practical information:
- Sessions will take place in EIETL, during week(s) [xxx].
- This activity involves preliminary work-- reading the lab handout ([estimated duration: 1 hour]).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
For Physical-layer communications (first 13L):
- B. Rimoldi, Principles of Digital Communication: A Top-Down Approach, Cambridge University Press, 2016]
- R. Gallager, Principles of Digital Communication, Cambridge University Press, 2008
- U. Madhow, Fundamentals of Digital Communication, Cambridge University Press, 2008
For network algorithms (last 3L):
- R. Srikant and L. Ying, Communication Networks, Cambridge University Press, 2014.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 18/02/2018 16:43
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2022-23
Module Leader
Lecturers
Prof S.S. Singh, Prof S. J. Godsill
Lab Leader
Prof S Godsill
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Study more advanced probability theory, leading into random process theory.
- Study random process theory and focus on discrete time methods.
- Introduce inferential methodology, including maximum likelihood and Bayesian procedures, and examples drawn from signal processing. Objectives
Objectives
As specific objectives, by the end of the course students should be able to:
- By the end of the course students should be familiar with the fundamental concepts of statistical signal processing, including random processes, probability, estimation and inference.
Content
Lectures 1-8: Advanced Probability and Random Processes
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
Example inference models: frequency estimation, AR model, Estimation of parameters for discrete Markov chain.
Coursework
Random variables and random number generation
Learning objectives:
- Understand random variables and functions of random variables and their simulation
- To study the Jacobian as used with random variables
- To experiment with methods for non-uniform random number generation
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity involves preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 23/11/2022 08:40
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