Image Features, Hough Transform Image Pyramid CSE399b, Spring 06 Computer Vision Lecture 10

Boundary and Edge: Edge detection-> lines

An example: S.F. in fogS.F. in Canny

An example: S.F. in fogS.F. with Hough lines

Hough Transform image edges needs to be grouped into lines and junctions Hough transform: Detect lines in an edge image

Line Representation is the distance from the origin to the line is the norm direction of the line Image space : Hough space : point in image space ==> a curve in hough space

Line Representation is the distance from the origin to the line is the norm direction of the line Image space : Hough space : point in image space ==> a curve in hough space For every theta, set:

Hough Space point in hough space ==> line in image space

Intersection of the curves Each pixel in the image => One curve in Hough space What is the intersection of the curves?

Hough Transform Points in the line : In hough space, all the curves pass: So the intersection of the curves is the parameters of the line! Next question: How to find the intersection ?

Voting Scheme Each edge pixel in the image votes in Hough space for a series of Choose the of maximum votes

Basic Hough Transform

Example

Extension Choose the sampling of Use gradient of the image voting for specific Iteratively find the maximum votes and remove corresponding edge pixels Suppress edge pixels close to the detected lines

Example of Using Estimated Edge Orientation+Iterative line removal

A detour through scale space

Image encoding-decoding 1) Image statistics: pixel in neighborhood are correlated, encode per pixel value is redundant 2) Predictive Coding:use raster scan, predict based on pass value, and store only the error in prediction. Simple and fast signal prediction Error-encoded

Non-causal prediction non-causal involves typically transform, or solution to a large sets of equations. Encode block by block. Bigger compression but slower signal prediction Error-encoded

Gaussian Pyramid for encoding 1)Prediction using weighted local Gaussian average 2)Encode the difference as the Laplacian 3)Both Laplacian and the Averaged image is easy to encode [Burt & Adelson, 1983]

Gaussian pyramid

Choice in weighting function Gaussian

Image Expansion

+ - Laplaican Image

Gaussian pyramid is smooth=> can be subsampled Laplacian pyramid has narrow band of frequency=> compressed

Ln = Gn