Mathematical Computing for Medical Imaging

IIDS67462 Mathematical Computing for Medical Imaging 15 Semester 2 Postgraduate Taught Level 6 Timothy Cootes Unit coordinator Division of Informatics, Imaging and Data Sciences 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 This unit will introduce mathematical and computing techniques used in medical image analysis. It will cover optimsation techniques, statistical shape modelling, classification/regression and an introduction to neural networks.  Examples from a range of medical image analysis problems will be included.   Students will learn how the different algorithms work, but more importantly, when to use each approach.  The course includes both the mathematical techniques and an introduction to Python libraries which implement them.  Students will learn Python programming skills in order to write software to solve practical problems.     Optimisation techniques:<ul> <li>One dimensional, multi-dimensional</li> <li>Local techniques with and without derivatives</li> <li>Global techniques</li></ul>Statistical shape and appearance models:<ul> <li>Mathematical definitions</li> <li>Examples of use</li> <li>Matching to images</li></ul>Classification and regression techniques:<ul> <li>Basic theory</li> <li>Evaluating classfiers using ROC curves</li> <li>Linear Discriminant Analysis, k-Nearest Neighbours </li> <li>Random Forests</li> <li>Neural Networks</li></ul>Dimensionality Reduction<ul> <li>PCA</li> <li>Local Linear Embedding</li> <li>t-SNE</li> <li>Auto-encoders</li></ul>Convolutional Neural Networks:<ul> <li>Theory and training</li> <li>Examples of use for classification, segmentation and point finding  </li></ul>  The unit aims to: •    Introduce concepts of programming in key areas of Medical Image Computing •    Introduce key mathematical and statistical concepts and methods appropriate to the quantitative analysis of medical images.On successful completion of the unit, students should •    Understand the key mathematical concepts and computing tools for extracting information from medical images. •      Have developed skills in evaluation of algorithms for the purposes of understanding publications in this area and so contribute to the available pool of new <ul> <li>Understand the key mathematical concepts and computing tools for extracting information from medical images.</li> <li>Have developed skills in evaluation of algorithms for the purposes of understanding publications in this area and so contribute to the available pool of new researchers. </li></ul>  A1  Understand key mathematical techniques useful for medical imaging and image analysis, including optimisation, shape/appearance modelling, classification and regression methods A2 Understand and be able to use optimisation techniques A3 Understand shape and appearance models A4 Understand and be able to use classification and regression methods B1 The ability to turn algorithm specifications into codeB2 The ability to choose the most appropriate technique to solve various mathematical problems   C1 To be able to write Python code to solve mathematical problems C2 To be familiar with key Python libraries (NumPy, SciPy and PyTorch) D1 Use originality to solve mathematical problems using software D2 Familiarity with writing programs using the Python language Analytical skills Problem solving Written communication Other Programming (Python) Skills Each session will include  a)    Approximately 90 minutes of taught material (also available broken down into 3-10 minute videos on Blackboard) interspersed with mathematical problems illustrating some of the ideas. b)    A hands-on practical section in which it is shown how mathematical ideas introduced in the lectures are implemented using Python libraries. Students should try the examples on their own laptops and are given in-class challenges. c)    A programming challenge on some aspect of the work to be done before the next session (some of these will be assessed)  0 Other 40% 1 Written exam 60% <figure class="table" style="float:left;"><table class="MsoNormalTable" style="border-collapse:collapse;mso-border-alt:solid windowtext .5pt;mso-border-insideh:.5pt solid windowtext;mso-border-insidev:.5pt solid windowtext;mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-table-layout-alt:fixed;" border="1" cellspacing="0" cellpadding="0" width="640"><tbody><tr style="mso-yfti-firstrow:yes;mso-yfti-irow:0;"><td style="border:1.0pt solid windowtext;mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:218.05pt;" width="291">Assessment task<o:p></o:p></td><td style="border-bottom-style:solid;border-color:windowtext;border-left-style:none;border-right-style:solid;border-top-style:solid;border-width:1.0pt;mso-border-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:77.95pt;" width="104">Length<o:p></o:p></td><td style="border-bottom-style:solid;border-color:windowtext;border-left-style:none;border-right-style:solid;border-top-style:solid;border-width:1.0pt;mso-border-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:4.0cm;" width="151">How and when feedback is provided<o:p></o:p></td><td style="border-bottom-style:solid;border-color:windowtext;border-left-style:none;border-right-style:solid;border-top-style:solid;border-width:1.0pt;mso-border-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:70.9pt;" width="95">Weighting within unit (if relevant)<o:p></o:p> </td></tr><tr style="mso-yfti-irow:1;"><td style="border-bottom-style:solid;border-color:windowtext;border-left-style:solid;border-right-style:solid;border-top-style:none;border-width:1.0pt;mso-border-alt:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:218.05pt;" width="291">Formative<o:p></o:p>1 Programming challenge (to demonstrate the student’s ability to solve practical problems by writing Python scripts and to present the results clearly)<o:p></o:p></td><td style="border-bottom:1.0pt solid windowtext;border-left-style:none;border-right:1.0pt solid windowtext;border-top-style:none;mso-border-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:77.95pt;" width="104"> </td><td style="border-bottom:1.0pt solid windowtext;border-left-style:none;border-right:1.0pt solid windowtext;border-top-style:none;mso-border-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:4.0cm;" width="151"> </td><td style="border-bottom:1.0pt solid windowtext;border-left-style:none;border-right:1.0pt solid windowtext;border-top-style:none;mso-border-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:70.9pt;" width="95"> </td></tr><tr style="height:3.0pt;mso-yfti-irow:2;mso-yfti-lastrow:yes;"><td style="border-bottom-style:solid;border-color:windowtext;border-left-style:solid;border-right-style:solid;border-top-style:none;border-width:1.0pt;height:3.0pt;mso-border-alt:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;padding:0cm 5.4pt;vertical-align:top;width:218.05pt;" width="291">Summative<o:p></o:p>1 Programming challenge (to demonstrate the student’s ability to solve practical problems by writing Python scripts and to present the results clearly)<o:p></o:p> 2 Final written Exam (2 hrs) <o:p></o:p></td><td style="border-bottom:1.0pt solid windowtext;border-left-style:none;border-right:1.0pt s <ul> <li> Formal summative assessments </li> <li> Real time educative formative assessments during practical classes</li> </ul> Students are assumed to have a basic knowledge of linear algebra (matrices and vectors) and basic calculus (e.g. derivatives).  Introductory material covering what is assumed is included on-line. MSc Health Data Science PT MSc Health Data Science PGDT Taught Component Optional PG Dip Health Data Science PT PG Diploma Health Data Science PGDT Taught Component Optional MSc Health Data Science FT MSc Health Data Science FT PGDT Taught Component Optional PG Dip Health Data Science FT PG Dip Health Data Science FT PGDT Taught Component Optional MSc Medical Imaging Science FT MSc Medical Imaging Science FT PGDT Taught Component Mandatory MSc Medical Imaging Science PT MSc Medical Imaging Science PT PGDT Taught Component Mandatory PG Dip Medical Imaging Science PG Dip Medical Imaging Science PGDT Taught Component Mandatory PG Dip Medical Imaging Science PG Dip Medical Imaging Science PGDT Taught Component Mandatory N 0 0 150