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Visual Perception Modeling: Geometric Operations and Linear Filters

Explore the spatial relationships and transformations in images through geometric operations and learn about the characteristics and applications of linear filters in visual perception modeling.

juanitarobertson
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Visual Perception Modeling: Geometric Operations and Linear Filters

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  1. Outline • Announcement • Homework #1 • Local operations (continued) • Geometric operations • Linear filters

  2. Announcement • Homework #1 Visual Perception Modeling

  3. Geometric Operations • Geometric operations change the spatial relationships among the objects in an image • Have an image on a rubber sheet and then deform the sheet • A geometric operation is more general in that it can move any point in the input image to any point in the output image Visual Perception Modeling

  4. Geometric Operations – cont. • Two separate algorithms • Spatial transformation • An algorithm that defines the spatial transformation itself • This specifies the motion of each pixel • Pixel value interpolation • Integer pixel positions can map to fractional positions • Nearest neighbor interpolation • Bilinear interpolation • Implementation issues Visual Perception Modeling

  5. Spatial Transformation • Simple transformations • Rotation • Scaling • Affine transformation • General transformations • Specified by the motion of each pixel • Called “optical flow” • Specified by control points Visual Perception Modeling

  6. Applications of Geometric Operations • Geometric calibration • Remove the camera-induced geometric distortion from digital images • Image rectification • Transform images of non-rectangular pixel coordinates to display systems Visual Perception Modeling

  7. Applications of Geometric Operations – cont. • Image registration • Register similar images for purposes of comparison • Motion estimation and video analysis Visual Perception Modeling

  8. Image Mosaicing • Remote sensing of earth and planets, panoramas .... • More on the web • Image mosaics from CMU Visual Perception Modeling

  9. Applications of Geometric Operations – cont. • Model-based object recognition • Transform an object model to match the input image Visual Perception Modeling

  10. Applications of Geometric Operations – cont. • Map projection • Project images for purposes of mapping • How to produce photo-mosaic maps of the Earth, moon, or the planets • Cartography • Produce two-dimensional maps of spherical or ellipsoidal bodies • Map properties • Cartographic projections Visual Perception Modeling

  11. Applications of Geometric Operations – cont. • Image morphing • A technique that allows one object to transform gradually into another • Generate a movie sequence from two images • Image interpolation • How to generate a realistic looking transformation • It has tremendous commercial values Visual Perception Modeling

  12. Image Morphing Visual Perception Modeling

  13. An Example Visual Perception Modeling

  14. Image Morphing Visual Perception Modeling

  15. More Examples on the Web • On the web • http://www.cis.ohio-state.edu/graphics/kf/morph_example.html Visual Perception Modeling

  16. Research Problems • How to create a model very efficiently • Identify important features in one image and the corresponding features in the other image • Deformable templates • Specify the deformation for certain effects • Facial expression modeling Visual Perception Modeling

  17. Linear System Theory • What is a system? • A system is anything that accepts an input and produces an output in response y[n] = T{x[n]} where x[n] is the input sequence and y[n] is the output sequence in responses to x[n] • How to represent a sequence? Visual Perception Modeling

  18. Linear System • Linearity • y1[n] = T{x1[n]} • y2[n] = T{x2[n]} • Then • y1[n]+y2[n] = T{x1[n]+x2[n]} Visual Perception Modeling

  19. Shift-Invariant System • Shift invariance • y[n] = T{x[n]} • y[n-T] = T{x[n-T]} • LSI system • A LSI system is completely characterized by its impulse response h[n] • For any other input, we can obtain the response through convolution Visual Perception Modeling

  20. Filtering • Closely related to convolution • Filter examples • Smoothing by averaging • Smoothing by Gaussian Visual Perception Modeling

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