Image Processing and Analysis (ImagePandA) 9 – Shape Christoph Lampert / Chris Wojtan

Outline Representation Boundary following Signatures R(theta) Convex deficiency Skeletons Shape Descriptors Boundary Fourier descriptors Statistical Moments Regional Simple: area, permieter, ratio, … Topology (Euler characteristic) E = C-H Statistical Moments Moment Invariants Morphing Blending Morphing Level set methods 2

Overview Want to be able to compare and describe shapes and images Need meaningful geometric representations Need metrics which are similar for similar images Boundary description Shape of boundary/border Region description Color/texture/stuff within shape 3

Simple metrics Area Perimeter Ratio between Area & Perimeter CS 484, Fall 2012©2012, Selim Aksoy4

Boundary following 5

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Distance vs. Angle signature 8 Invariant to translation, scale, and rotation Assuming: start from centroid, consistently pick starting point

Distance vs. Angle signature 9

10 Invariant to translation, scale, and rotation, assuming: start from centroid How would you compute the centroid? consistently pick starting point eg farthest from centroid Parameterize by angle so # of pixels is irrelevant

Convex defficiency 11

Convex defficiency 12

Skeletons 13

Moment Invariants 14

Moment Invariants 15

Moment Invariants 16

Moment Invariants 17

Moment Invariants 18