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

Visual Perception Modeling Announcement Homework #1 11/8/2018 Visual Perception Modeling

Visual Perception Modeling 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 11/8/2018 Visual Perception Modeling

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 11/8/2018 Visual Perception Modeling

Spatial Transformation Simple transformations Rotation Scaling Affine transformation General transformations Specified by the motion of each pixel Called “optical flow” Specified by control points 11/8/2018 Visual Perception Modeling

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 11/8/2018 Visual Perception Modeling

Applications of Geometric Operations – cont. Image registration Register similar images for purposes of comparison Motion estimation and video analysis 11/8/2018 Visual Perception Modeling

Visual Perception Modeling Image Mosaicing Remote sensing of earth and planets, panoramas .... More on the web Image mosaics from CMU 11/8/2018 Visual Perception Modeling

Applications of Geometric Operations – cont. Model-based object recognition Transform an object model to match the input image 11/8/2018 Visual Perception Modeling

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 11/8/2018 Visual Perception Modeling

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 11/8/2018 Visual Perception Modeling

Visual Perception Modeling Image Morphing 11/8/2018 Visual Perception Modeling

Visual Perception Modeling An Example 11/8/2018 Visual Perception Modeling

Visual Perception Modeling Image Morphing 11/8/2018 Visual Perception Modeling

More Examples on the Web http://www.cis.ohio-state.edu/graphics/kf/morph_example.html 11/8/2018 Visual Perception Modeling

Visual Perception Modeling 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 11/8/2018 Visual Perception Modeling

Visual Perception Modeling 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? 11/8/2018 Visual Perception Modeling

Visual Perception Modeling Linear System Linearity y1[n] = T{x1[n]} y2[n] = T{x2[n]} Then y1[n]+y2[n] = T{x1[n]+x2[n]} 11/8/2018 Visual Perception Modeling

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 11/8/2018 Visual Perception Modeling

Visual Perception Modeling Filtering Closely related to convolution Filter examples Smoothing by averaging Smoothing by Gaussian 11/8/2018 Visual Perception Modeling