The Hough transform is a feature extraction

technique used in image analysis, computer

vision, and digital image processing. The

purpose of the technique is to find imperfect

instances of objects within a certain class of

shapes by a voting procedure.

More accurately,

Simple Visual Instance Of Hough Transform

Hough-transform is best known as a method "to find

Straight Lines" in an image. Unfortunately, people who

encounter the concept for the first time.

Hough-transform Visualize Instance of Edges

Hough-transform

Visualize Instance

of Face Indeed

It was initially invented for machine analysis of bubble chamber photographs (Hough, 1959).

The Hough transform was patented as “U.S. Patent 3,069,654” in 1962 and assigned to the U.S. Atomic Energy Commission with the name "Method and Means for Recognizing Complex Patterns". This patent uses a slope-intercept parameterization for straight lines, which awkwardly leads to an unbounded transform space since the slope can go to infinity.

And at first used to find lines in images a

decade later by Duda in 1972.

o The goal is to find the location of lines in images.

o This problem could be solved by e.g. Morphology and a linear structuring element, or by correlation.

o We would need to handle rotation, zoom, distortions etc.

o Hough transform can detect lines, circles and other structures if their parametric equation is known.

o It can give robust detection under noise and partial occlusion.

As a simple example, consider the common problem of fitting a set of line segments to a set of discrete image points (e.g. pixel locations output from an edge detector).Following Figure shows some possible solutions to this problem. Here the lack of a priori knowledge about the number of desired line segments (and the ambiguity about what constitutes a line segment) render this problem under-constrained.

Figure:a) Coordinate points. b) and c) Possible straight line fittings.

We can analytically describe a line segment in a

number of forms. However, a convenient

equation for describing a set of lines uses

parametric or normal notion:

Where “r” is the length of a normal from the

origin to this line and “θ” is the orientation of

with respect to the X-axis. (See Figure 2.) For

any point “(x,y)” on this line, “r” and “θ” are

constant.

Figure 2: Parametric description of a straight

line.

o The input image must be a thresholded edge

image.

o The magnitude results computed by the Sobel

o Operator can be thresholded and used as input.

Thresh Holed Edges

Prior to applying Hough transform:

Compute edge magnitude from input image.

As always with edge detection, simple lowpass

filtering can be applied first.

Threshold the gradient magnitude image.

Prior to applying Hough transform:

Quantize the parameter space (a,b), that is, divide it into cells.

This quantized space is often referred to as the accumulator cells.

In the figure in the next slide a(min) is the minimal value of a cell.

Count the number of times a line intersects a given cell.

– For each point (x,y) with value 1 in the binary image, find the values of (a,b) in the range [a(min),a(max)],[b(min),b(max)] defining the line corresponding to this point.

– Increase the value of the accumulator for

these (a',b') point.

– Then proceed with the next point in the

image.

Cells receiving a minimum number of “votes”

are assumed to correspond to lines in (x,y)

space.

– Lines can be found as peaks in this

accumulator space.

Here I want to Finish my

Presentation about Hough

Transform.

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