1Ellen L. Walker Segmentation Separating “content” from background Separating image into parts corresponding to “real” objects Complete segmentation Each part corresponds to a real object No overlapping parts Partial segmentation Regions of homogeneous brightness, texture, color, etc. Overlapping parts, needs further processing

2Ellen L. Walker Segmentation Methods Based on global knowledge Thresholding based on histogram Edge-based Region-based Combinations of the last two Edge-based and region-based are duals of each other

3Ellen L. Walker Thresholding Fixed threshold “empirically determined” = trial & error Global vs. positional Upper, lower or both (band thresholding) Generalize to any number (table: intensity -> label) Image-dependent threshold Histogram based - look for minimum between 2 maxima Find highest local maxima if more than two Apply techniques similar to edge detection!

4Ellen L. Walker Thresholding with Hysteresis Two thresholds Global (higher) -- any pixel above this is “good” Local (lower) -- pixels above this are “good” if they have “good neighbors” Neighborhoods 4-connected = N, S, E, W 8-connected = NE, N, NW, E, W, SE, S, SW Others for non-square grids (triangles, hexagons)

5Ellen L. Walker Taking advantage of hierarchy Works for thresholding and all kinds of segmentation “Coarse to fine” segmentation Create images at multiple scales (hierarchical representation) Segment at coarse scale Map segments to finer scale & use as starting points

6Ellen L. Walker Edge-based segmentation Preprocessing the edges thresholding the edge image Non-maximal suppression (don’t keep me if my neighbor across the edge is stronger) Hysteresis Let edges “influence” each other (relaxation)

7Ellen L. Walker Relaxation Goal: Use context to help overcome effects of noise Given: A set of nodes with values A neighborhood relation An update rule Find a “stable” set of values (applying the update rule again will not cause changes)

8Ellen L. Walker Relaxation Algorithm Initialize nodes (by preprocessing or random) initial edge detection Compute values at nodes edge confidence level c (0) (e) Update values at nodes according to update rule c (k+1) (e) = min(1, c (k) (e)+∂) or max(0, 1, c (k) (e)–∂) Count neighbor edges to determine ∂ and direction Stop at convergence (no more change) All confidences at 0 or 1

9Ellen L. Walker Hough Transform Given marked edge pixels, find examples of specific shapes Line segments Circles Generalized shapes (GHT) Basic idea - Patented 1962 Every edge pixel is a point that votes for all shapes that pass through it. Votes are collected in “parameter space” - look for peaks “Parameter space” is a k-D histogram!

10Ellen L. Walker Hough Transform for Lines Parameter space: Ax+By+C = 0(But A,B, C aren’t unique!) Divide by sqrt(A*A+B*B); first two terms are sin,cos of the angle Angle, distance from 0 Angle = arctan(A/B), distance = C/(A*A+B*B) Given a point (x0,y0), find all theta, distance pairs cos(theta)*x0 + sin(theta)*y0 + distance = 0

11Ellen L. Walker Hough Transform for Lines (cont.) Increment all “cells” in p-space through which curve passes

12Ellen L. Walker Hough Transform for Circles Parameter space is (centerx, centery, radius) Update: For every point, computer center, radius of all circles passing through the point Mark each center, radius pair Alternative computation: for each cell, compute distance from that cell to point - increment if close enough.

13Ellen L. Walker GHT: Generalized Hough Transform Parameters are translation, rotation & scale of a fixed 2D shape,represented as a point set Given a point and a location in the transform space, if the point is in (or close enough to a point in) the transformed point set, then record a vote.

14Ellen L. Walker Hough Transform Issues Space usage Need large arrays for accurate results! More complex objects need more parameters (fast!) Peak detection Large spaces take long to search - threshold unreliable “Accidental peaks” are not unusual Noise causes “cluster” rather than “peak” - may need to use cluster detection (remember K-means?) Easily parallelizable!!