Image Features, Hough Transform

Image Pyramid

CSE399b, Spring 06

Computer Vision

Lecture 10

http://www.quicktopic.com/35/H/NHVD8SZQQJHZ

Boundary and Edge: Edge detection-> lines

An example:

S.F. in fog S.F. in Canny

An example:

S.F. in fog S.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 fora series of

• Choose the of maximum votes

Basic Hough Transform

Example

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

1010 20 22 24 24

1010 15 21 23 24

signal

prediction

00 5 1 1 0Error-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.

1010 20 22 24 24

1310 17 22 23 24

signal

prediction

20 3 0 1 0Error-encoded

Gaussian Pyramid for encoding

1) Prediction using weighted local Gaussian average2) Encode the difference as the Laplacian3) Both Laplacian and the Averaged image is easy to encode

[Burt & Adelson, 1983]

Gaussian pyramid

Choice in weighting function

Gaussian

Image Expansion

Image Expansion

+ -

Laplaican Image

Gaussian pyramid is smooth=> can be subsampled

Laplacian pyramid has narrow band of frequency=> compressed

Ln = Gn