CS6640 – Project 3 Image TransformationsAssigned Oct. 6, 2010Due Oct. 27 (Just before midnight)Instructor: Guido GerigTA: Miaomiao ZhangGoalsThe purpose of this assignment is to learn about linear and nonlinear image transformations (warping).Please read following instructions carefully.1 Affine Image TransformationImplement a program that transforms an image given an affine transformation (6 parameters), which includesrotation, translation, scaling and shear. Please note that the transformation is generally applied from thetarget image backwards to the source image, i.e. you step through each pixel of the new image, determinethe position in the source image, and take/calculate the intensity at this pixel to be used for the targetimage. Two types of interpolations need to be implemented:1. Nearest neighbor (NN): Take the intensity from the pixel which is closest to the non-grid position of thetransformation. Please note that this can be easiest achieved by rounding a non-grid (x,y)-ccordinateto the next integer coordinates.2. Implement bilinear interpolation from the 4 neighbors of the non-grid coordinate, folling the discussionin the course.Take an input image of your choice and apply:1. Separate translation, rotation, scaling, shear,2. An affine transformation with 6 parameters.3. For the affine transformation, apply NN and bilinear interpolation and show the differences (you couldlook at a part that is strongly zoomed (which can be calculated with your scaling transform).2 Calculation of affine transform from landmarksAs discussed in the course, a transformation can be determined based on a set of corresponding landmarks ina source and a target image. A minimum of 3 points with (x,y) coordinates is required, but more landmarksresult in a more stable solution by solving an overconstrained linear equation system. Please note that youcan use Matlab help and Mathworks web-based help for hints on solutions.• Implement a module that determines a pixel position with the mouse.• Use this module to create sets of corresponding pixel positions in a source and a target image.• Set up the linear equation system and implement a solution to solve for the affine transformationbetween the source and target image.• Apply the transformation and and check for the correctness of the result by displaying source, targetand resulting images side by side. You can even create another result by blending the result and sourcetogether (e.g. adding the images) to have some visual check of geometry differences.1As test images, you can use own pictures (e.g. of frontal view of faces of humans or animals). Wouldsuch pictures not be available, you can search the web (e.g. http://www.face-rec.org/databases/). You canbe creative about the choice of images, applications as shown in the course slides are for example lip readingin video sequences or normative atlas building in medicine.3 Calculation of nonlinear warping using radial basis functionsNote: Only start this section after successful completion of the two sections above!As discussed in class and explained on the course slides, you can warp images based on sets of cor-responding landmarks via a nonlinear transformation that uses radial basis functions (RBFs). You cansee that elements of code developed in the previous sections will be the same, such as determining sets ofcorresponding landmarks and solving a linear equation system.Following the course notes, setup a linear equation system based on RBFs for image warping and choosea strategy for solving the system (e.g. Matlab functions).• Determine a set of corresponding landmarks.• Choose a Gaussian kernel for the function Φ(¯x) where the Gaussian width σ is your free parameter.• Setup the equation system, solve for the parameters.• Given the solution, transform the image.• Experiment with different sets of landmarks (e.g. one only up to a few) and with a given set oflandmarks, a few Gaussian widths.• Show resulting images and discuss.4 Instructions, Requirements, and Restrictions1. Please use your name “NAME” in all reportts and submitted materials to uniquely identify yourprojects.2. Write your project code in a single directory, called project1-NAME.3. For Matlab each individual function (including functions you define) should be a “.m” file, and yourfunctions should call one another as necessary.4. We do not allow to use Matlab toolbox functions (e.g. Imaging Toolbox) or other existing imageprocessing libraries in order to give all students the same conditions for code development1.5. You should have in your report a short description of each algorithm you used and documentation onhow your code is organized. Failure to do this will result in a loss of points. Please remmember to addyour name to the report title.6. Your project report will be in the form of an html file called index.html, contained in that directory.All links from that file must be relative and all other files necessary to read your report must be inthat directory (or subdirectories).7. You should use examples of images in your report. They should be viewable in the browser when weopen your html file.1The core MATLAB package comes with several rudimentary functions that can b e used to load, save, and perform customfunctions on images. Taken from wikibooks28. You will submit a single tar file created from from your project directory with the unix command tar-czf project1-NAME.tgz./project1-NAME.9. Please remember or look-up the honor code and requirement to provide your own solution as discussedin the syllabus.10. Please look up the late policy as defined in the