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Computer and Robot Vision II. Chapter 18 Object Models And Matching. Presented by: 傅楸善 & 徐子凡 0989306249 r98922132@ntu.edu.tw 指導教授 : 傅楸善 博士. 18.1 Introduction. object recognition: one of most important aspects of computer vision. Joke. 18.2 Two-Dimensional Object Representation.

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## Computer and Robot Vision II

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**Computer and Robot Vision II**Chapter 18 Object Models And Matching Presented by: 傅楸善 & 徐子凡 0989306249 r98922132@ntu.edu.tw 指導教授: 傅楸善 博士 Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C.**18.1 Introduction**• object recognition: one of most important aspects of computer vision DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.2 Two-Dimensional Object Representation**• 2D shape analysis useful in machine vision application: • medical image analysis • aerial image analysis • manufacturing DC & CV Lab. CSIE NTU**18.2 Two-Dimensional Object Representation**• 2D shape representation classes: • 18.2.1 global features • 18.2.2 local features • 18.2.3 boundary description • 18.2.4 skeleton • 18.2.5 2D parts DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• 2D object: • can be thought of as binary image • value 1: pixels of object • value 0: pixels outside object • 2D shape features: • area, perimeter, moments, circularity, elongation DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• Shape Recognition by Moments • : binary image function • : 2D shape • digital th moment of : • area of S • number of pixels of S DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• moment invariants • are functions of digital moments invariant under certain shape transformations. • translation, rotation, scaling, skew • center of gravity of S: DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• central th moment of S: • central moments: translation invariant • normalized central moments of S: DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• seven functions that are rotation invariant DC & CV Lab. CSIE NTU**Original**Half Size Mirrored Rotated 2° Rotated 45° DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• Fourier descriptors: • another way for extracting features from 2D shapes • defined to characterize boundary • The main idea is to represent the boundary as a function of one variable , expand in its Fourier series, and use the coefficients of the series as Fourier descriptors (FDs). • finite number of FDs: can be used to describe the shape DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• Each coordinate pair can be treated as a complex number so that • Discrete Fourier transform of is DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• The complex coefficients are called the Fourier descriptors of the boundary. • The inverse Fourier transform of these coefficients restores . • Suppose, only the first P coefficients are used. DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**DC & CV Lab. CSIE NTU**18.2.1 Global Feature Representation**• Some basic properties of Fourier descriptors. • Notation: Impulse function : DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.2.2 Local Feature Representation**• 2D object characterized by: • local features, attributes, relationships • most commonly used local features: • Holes • found by connected component procedure followed by boundary tracing • detected by binary mathematical morphology, if hole shapes known • properties: areas, shapes • Corner • detection: can be performed on binary or gray tone image • property: angle at which lines meet DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• boundary representation: • most common representation for 2D objects. • 3 main ways to represent object boundary: • sequence of points • chain code • sequence of line segments DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• The Boundary as a Sequence of Points • boundary points from border-following or edge-tracking algorithms • interest points: boundary points with special property useful in matching DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• The Chain Code Representation • chain encoding: • can be used at any level of quantization • saves space required for row and column coordinates • boundary encoded: • first quantized by placing over square grid • square grid side length: • determines resolution of encoding • marked points: • grid intersections closest to curve and used in encoding • ＊: • marks starting point of curve DC & CV Lab. CSIE NTU**chain encoding of boundary curve**DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• line segments: links: to be used to approximate the curve • encoding scheme: eight possible directions assigned integer between 0, 7 • chain: chain encoding: in the form DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• length of chain code with n chains: • can be simply estimated as n • no: number of odd chain codes • ne: number of even chain codes • nc: number of corners • L: unbiased estimate of perimeter length • Freeman suggested: DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• The Boundary as a Sequence of Line Segments • line segment sequence: after boundary segmented into near-linear portion • line segment sequence: used in shape recognition or other matching tasks • : coordinate location where pair of lines meet • : angle magnitude where pair of lines meet • sequence of junction points to represent line segment sequence DC & CV Lab. CSIE NTU**18.2.3 Boundary Representation**• sequence of junction points representing test object T • an association • goal: given O, T, to find F satisfying i < j F(i) < F(j) or F(i) = missing or F(j) = missing DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.2.4 Skeleton Representation**• strokes: long, sometimes thin parts forming shapes DC & CV Lab. CSIE NTU**18.2.4 Skeleton Representation**• symmetric axis transform: • set of maximal circular disks that fit inside object • symmetric axis: • locus of centers of these maximal disks DC & CV Lab. CSIE NTU**18.2.4 Skeleton Representation**• The symmetric axis is one example of a skeleton description of 2D object. • symmetric axis is not always completely representative of the strokes of an object. • rectangle: consists of five line segments not single line • symmetric axis: extremely sensitive to noise make it difficult to use in matching. DC & CV Lab. CSIE NTU**18.2.4 Skeleton Representation**• local symmetry: midpoint P of line segment BA • α: angle between BA and outward normal Na at A • α: angle between BA and inward normal Nb at B DC & CV Lab. CSIE NTU**18.2.4 Skeleton Representation**• The loci of local symmetries that are maximal w.r.t. forming a smooth curve are called axes or spines. • cover of axis: portion of shape subtended by axis • axis cover properly contained in another cover: second axis subsumes first The short diagonal axes are subsumed by the horizontal and vertical axes and can be either deleted or relegated to a lower place in a hierarchical description of the shape (Chap. 19). DC & CV Lab. CSIE NTU**18.2.4 Skeleton Representation**• Axes of smoothed local symmetries of several objects. DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.2.5 Two-Dimensional Part Representation**• parts, attributes, interrelationships: form structural description of shape • nuclei: regions where primary convex subset overlap nuclei DC & CV Lab. CSIE NTU**18.2.5 Two-Dimensional Part Representation**• near-convexity: allows noisy distorted instances to have same decompositions • P1 , P2: two points on object boundary • LIrelation: visibility relation • if line completely interior to object boundary, • Apply the graph-theoretic clustering algorithm to determine clusters of visibility relation DC & CV Lab. CSIE NTU**18.2.5 Two-Dimensional Part Representation**• decomposition of three similar shapes into near-convex pieces DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.3 Three-Dimensional Object Representations**• 18.3.1 Local Features Representation. • 18.3.2 Wire Frame Representation. • 18.3.3 Surface-Edge-Vertex Representation. • 18.3.4 Stick, Plates, and Blobs. • 18.3.5 Generalized Cylinder Representation. • 18.3.6 Super-quadric Representation. • 18.3.7 Octree Representation. • 18.3.8 The Extended Gaussian Image. • 18.3.9 View-Class Representation. DC & CV Lab. CSIE NTU**18.3.1 Local Features Representation**• Local Features Representation • range data: • obtained from laser range finder, light striping, stereo, etc. • from depth, try to infer surfaces, edges, corners, holes, other features • 3D matching more difficult than 2D because of occlusion DC & CV Lab. CSIE NTU**Joke**DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• wire frame model: • 3D object model with only edges of object DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• two-color hyperboloid and its line drawing DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• Necker cube: lower-vertical face or upper-vertical face closer to viewer • Schroder staircase: viewed either from above or from below DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• general-viewpoint assumption: none of the following situations • 1. two vertices of scene objects represented at same picture point • 2. two scene edges seen as single line in picture • 3. vertex seen exactly in line with unrelated edge DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• general-viewpoint assumption: heart of line-drawing interpretation • viewpoint in perspective projection: center of projection • viewpoint in orthographic projection: direction of projection DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• subjective contours of Kanizsa: white occluding triangle in space DC & CV Lab. CSIE NTU**18.3.2 Wire Frame Representation**• line labels for visible projections of surface-normal discontinuities: DC & CV Lab. CSIE NTU

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