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Prepare for your image processing exam with this detailed study guide covering topics such as image filtering, edge detection, features, camera projection, mosaics, projective geometry, stereo vision, structure from motion, light perception, recognition algorithms, and more.

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Announcements

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  1. Announcements • Final is Thursday, March 20, 10:30-12:20pm • EE 037 • Sample final out today

  2. Filtering • An image as a function • Digital vs. continuous images • Image transformation: range vs. domain • Types of noise • Noise reduction by averaging multiple images • Cross-correlation and convolution • properties • mean, Gaussian, bilinear filters • Median filtering • Image scaling • Image resampling • Aliasing • Gaussian pyramids

  3. Edge detection • What is an edge and where does it come from • Edge detection by differentiation • Image gradients • continuous and discrete • filters (e.g., Sobel operator) • Effects of noise on gradients • Derivative theorem of convolution • Derivative of Gaussian (DoG) operator • Laplacian operator • Laplacian of Gaussian (LoG) • Canny edge detector (basic idea) • Effects of varying sigma parameter • Approximating an LoG by subtraction

  4. Features • What makes a good feature? • Derivation in terms of shifting a window • H matrix • Definition • Meaning of eigenvalues and eigenvectors • Harris operator • How to use it to detect features • Feature descriptors • MOPS (rotated square window) • SIFT (high level idea) • Invariance (how to achieve it) • Rotation • Scale • Lighting • Matching features • Ratio test • RANSAC

  5. Projection • Properties of a pinhole camera • effects of aperture size • Properties of lens-based cameras • focal point, optical center, aperture • thin lens equation • depth of field • circle of confusion • Modeling projection • homogeneous coordinates • projection matrix and its elements • types of projections (orthographic, perspective) • Camera parameters • intrinsics, extrinsics • types of distortion and how to model

  6. Mosaics • Image alignment • Image reprojection • homographies • spherical projection • Creating spherical panoramas • Handling drift • Image blending • Image warping • forward warping • inverse warping

  7. Projective geometry • Homogeneous coordinates and their geometric intuition • Homographies • Points and lines in projective space • projective operations: line intersection, line containing two points • ideal points and lines (at infinity) • Vanishing points and lines and how to compute them • Single view measurement • computing height • Cross ratio • Camera calibration • using vanishing points • direct linear method

  8. Stereo • Epipolar lines • Stereo image rectification (basic idea) • Stereo matching • window-based epipolar search • effect of window size • sources of error • Energy-minimization (MRF) stereo (basic idea) • Depth from disparity • Active stereo (basic idea) • structured light • laser scanning

  9. Structure from motion • Correcting drift in mosaics through global optimization • Least squares • Structure from motion • Solving for camera rotations, translations, and 3D points • The objective function • The pipeline (from Photo tourism slides: detection, matching, iterative reconstruction…) • Photo tourism

  10. Light, perception, and reflection • Light field, plenoptic function • Light as EMR spectrum • Perception • color constancy, color contrast • adaptation • the retina: rods, cones (S, M, L), fovea • what is color • response function, filters the spectrum • metamers • Finding camera response function (basic idea, not details) • Materials and reflection • what happens when light hits a surface • BRDF • diffuse (Lambertian) reflection • specular reflection • Phong reflection model • measuring the BRDF (basic idea)

  11. Photometric stereo • Shape from shading (equations) • Diffuse photometric stereo • derivation • equations • solving for albedo, normals • depths from normals • Handling shadows • Computing light source directions from a shiny ball • Limitations

  12. Recognition • Classifiers • Probabilistic classification • decision boundaries • learning PDF’s from training images • Bayes law • Maximum likelihood • MAP • Principle component analysis • Eigenfaces algorithm • use for face recognition • use for face detection

  13. Segmentation • Graph representation of an image • Intelligent scissors method • Image histogram • K-means clustering • Morphological operations • dilation, erosion, closing, opening • Normalized cuts method (basic idea)

  14. Motion • Optical flow problem definition • Aperture problem and how it arises • Assumptions • Brightness constancy, small motion, smoothness • Derivation of optical flow constraint equation • Lucas-Kanade equation • Derivation • Conditions for solvability • Relation to Harris operator • Iterative refinement • Newton’s method • Pyramid-based flow estimation

  15. Texture • Markov chains • Text synthesis algorithm • Markov random field (MRF) • Efros and Leung’s texture synthesis algorithm • Improvements • Fill order • Block-based • Texture transfer (basic idea)

  16. Guest Lectures • Richard Ladner—Tactile graphics • Jenny Yuen—cateract detection • Jeff Bigham—object-based image retrieval • (basic ideas)

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