Hough Transform

Omri Zorea and Alon Lipnik Group #11

Technique to find imperfect instances of object within a certain class of shapes. (i.e. lines, cycles, ellipses, parabolas etc.).

Use in image analysis, computer vision and digital image processing. Was invented by Richard Duda and Peter Hart in 1972 (patent of Paul Hough, 1962).

Introduction

Hough Transform

1. Aerial photo 2. X-Y plane 3. Hough plane

detecting transform

Hough Transform Find lines in picture (y = -mx + b).

Match dots on the picture to lines and match line to a dot.

The slope (m) can goes to infinity (unbounded domain) polar coordinates.

Hough Transform

Hough Transform

Detect arbitrary shapes in picture.

Each point in Image space is now a sinusoid:

ρ = x cosθ + y sinθ

For each edge point on image it compute his gradient and know

which shape is it.

Hough Transform

Hough Transform

Detect arbitrary shapes in picture.

Accumulator matrix - find lines with maximum points. determines Threshold values in matrix.

the values are the points-density of shape.

Parallel Algorithm

Hough Transform

The image is divided into rows with

the same number of columns.

PVM is a programming tool used for

the message routing, data

conversion and task scheduling.

Complexity of O(m*n^2).m – different

theta values.nxn – image

size

(* Algorithm LARPBS – linear array reconfigurable pipeline bus system)

Parallel Algorithm

Hough Transform

Speed Up:

Check on 4, 8, 16 and 32 processors.

Two different algorithms.

Image density range 5% - 15%.

Parallel Algorithm

Hough Transform

Efficiency:

Image density range from 5% to 25%.

Check on 4, 8, 12, 16 and 32 processors (process 0 is

the master).

Trade-Off (processors and image density).

Parallel algorithms for Hough Transform, Fevzi Oktay Ozbek : http://preserve.lehigh.edu/cgi/viewcontent.cgi?article=1073&context=etd A fast efficient parallel HT algorithm on LARPBS:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.99.8684&rep=rep1&type=pdf

Guillermo Sapiro of Duke university :https://www.youtube.com/watch?v=kMK8DjdGtZo

References