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Computer Vision, CS 763

Computer Vision, CS 763. Ajit Rajwade , CS 763, Winter 2014, IITB, CSE department. Why take this course?. Must if you want to do research work with us in computer vision or image processing

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Computer Vision, CS 763

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  1. Computer Vision, CS 763 AjitRajwade, CS 763, Winter 2014, IITB, CSE department

  2. Why take this course? • Must if you want to do research work with us in computer vision or image processing • Inherently interdisciplinary subject: numerous application areas - remote sensing, photography, visual psychology, archaeology, surveillance, etc. • Fast becoming a popular field of study in India: scope for R&D work in numerous research labs (In India: GE, Phillips, Siemens, Microsoft, HP, TI, Google; DRDO, ICRISAT, ISRO, etc.)

  3. Computer Vision and Image Processing: What’s the difference? • Difference is blurry • “Image processing” typically involves processing/analysis of (2D) images without referring to underlying 3D structure • Computer vision – typically involves inference of underlying 3D structure from 2D images • In computer vision, we will NOT study image enhancement, denoising, or compression. • Computer vision – direct opposite of computer graphics

  4. Computer Graphics 3D Models (point clouds with polygons connecting adjacent points) Image (2D entity) Computer Vision Image (2D entity) Image Processing Image (2D entity)

  5. Course web-page http://www.cse.iitb.ac.in/~ajitvr/CS763/

  6. What will we study in this course?

  7. (1) Camera Geometry • Relationship between object coordinates (given by a vector P in 3D) and image coordinates (given by vector p in 2D) • Effect of various intrinsic camera parameters (focal length of lens, nature of the lens, aspect ratio of detector array, etc) on image formation • Effect of various extrinsic camera parameters on image formation

  8. (1) Camera Geometry (continued) • Let’s say you take a picture of a simple object of known geometry (example: chessboard, cube, etc.). • Given the 3D coordinates of N points on the object, and their corresponding 2D coordinates in the image plane, can you determine the camera parameters such as focal length? • Answer is yes you can. This process is called as camera calibration.

  9. (1) Camera Geometry (Vanishing points) http://www.atpm.com/9.09/design.shtml

  10. (2) Shape from ‘X’ • An image is 2D. But most underlying objects are 3D. • Can you guess something about the 3D structure of the underlying object just given the 2D image? • The human visual system does this all the time. • We want to reproduce this effect computationally (the “holy grail” of computer vision)

  11. (2-A) Shape from Shading http://www.famouslogos.org/the-basics-of-three-dimensional-design http://www.psychol.ucl.ac.uk/vision/Lab_Site/Demos.html Image-based forensics?

  12. (2-B) Depth from Defocus

  13. (2-C) Stereo and Disparity http://www.cns.nyu.edu/~david/courses/perception/lecturenotes/depth/depth-size.html

  14. (3) Image Motion • Input: a video sequence • Desired Output: an estimate of the motion (2D) at all pixels in all frames • Applications of such an algorithm: object tracking, facial expression analysis, video stabilization, etc. • Typical assumptions: no change in illumination across frames, small motion between consecutive frames.

  15. http://www.jonathanmugan.com/GraphicsProject/OpticalFlow/ Aperture Problem: http://en.wikipedia.org/wiki/File:Aperture_problem_animated.gif

  16. (4) Image Mosaicing/Panoramas We will study an end-to-end technique for generating a panorama out of a series of pictures of a scene from different viewpoints. http://cs.bath.ac.uk/brown/autostitch/autostitch.html

  17. (5) Face Detection from Images We will learn a machine learning technique called boosting. We will study how this technique is applied for one particular classification problem: does a small rectangular region in an image contain a face or not?

  18. (6) Some “fundoo” topics • Image restoration in special settings. Example below. • Consider an object submerged in a water tub/tank. The object is imaged from outside (camera is not in water). The water surface is wavy and shaky, leading to distortions in the pictures. Can you remove these distortions?

  19. Mathematical Tools • Numerical linear algebra • Variational Calculus (also called calculus of variations) • Some machine learning methods • All these tools will be covered in class. Prior knowledge of these topics is not necessary.

  20. (1) Numerical linear algebra • Matrices and vectors – matrix inverse, eigenvectors and eigenvalues, singular value decomposition (SVD), matrix rank, matrix trace, etc.

  21. (2) Variational Calculus • Suppose you wanted to find the value of ‘x’ for which ‘f(x)’ is minimum (or maximum). • We compute ‘x’ by solving the equation f’(x) = 0. • There are many other methods of finding such an ‘x’. • The study of such techniques is called function optimization.

  22. (2) Variational Calculus • Now consider the question – given points A and B, there are infinitely many curves passing through these points. Which one of them has the least length? B Answer: Straight line segment. Question 2: What if the points A and B resided on a sphere? A

  23. (2) Variational Calculus • Consider the set of all closed curves having a fixed perimeter, say p. Which curve has the largest area amongst these? An elongated shape can be made more round while keeping its perimeter fixed and increasing its area. If a region is not convex, a "dent" in its boundary can be "flipped" to increase the area of the region while keeping the perimeter unchanged.

  24. (2) Variational Calculus • In both these questions, the answer is not one value ‘x’, but an entire curve (function). Such an optimization problem is called a calculus of variations problem. • We will use this tool in getting answers to some of the aforementioned computer vision problems.

  25. Programming tools • MATLAB and associated toolboxes • OpenCV (open source C++ library)

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