How to resolve the algorithm Hough transform step by step in the Julia programming language

Published on 22 June 2024 08:30 PM
#Julia

How to resolve the algorithm Hough transform step by step in the Julia programming language

Table of Contents

Problem Statement

Implement the Hough transform, which is used as part of feature extraction with digital images. It is a tool that makes it far easier to identify straight lines in the source image, whatever their orientation. The transform maps each point in the target image,

( ρ , θ )

{\displaystyle (\rho ,\theta )}

, to the average color of the pixels on the corresponding line of the source image (in

( x , y )

{\displaystyle (x,y)}

-space, where the line corresponds to points of the form

x cos ⁡ θ + y sin ⁡ θ

ρ

{\displaystyle x\cos \theta +y\sin \theta =\rho }

). The idea is that where there is a straight line in the original image, it corresponds to a bright (or dark, depending on the color of the background field) spot; by applying a suitable filter to the results of the transform, it is possible to extract the locations of the lines in the original image. The target space actually uses polar coordinates, but is conventionally plotted on rectangular coordinates for display. There's no specification of exactly how to map polar coordinates to a flat surface for display, but a convenient method is to use one axis for

θ

{\displaystyle \theta }

and the other for

ρ

{\displaystyle \rho }

, with the center of the source image being the origin. There is also a spherical Hough transform, which is more suited to identifying planes in 3D data.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Hough transform step by step in the Julia programming language

The given Julia code demonstrates the computation of a standard Hough transform on a binary image using the ImageFeatures package. Here's a detailed explanation:

  1. Importing the ImageFeatures Package:

    using ImageFeatures

    This line imports the ImageFeatures package, which provides functions for working with image features, including the Hough transform.

  2. Creating a Binary Image:

    img = fill(false,5,5)

    This creates a 5x5 binary image img filled with false values. It represents an image where all pixels are initially set to black.

  3. Drawing a Horizontal Line:

    img[3,:] .= true

    This line draws a horizontal line in the binary image at row 3. It sets all the values in the third row of the image to true, effectively turning on the pixels in that row, representing a horizontal line.

  4. Applying the Hough Transform:

    hough_transform_standard(img)

    This line applies the standard Hough transform to the binary image img. The Hough transform is a technique used to detect straight lines in an image. It converts the image into a parameter space, where each point represents a potential line in the original image.

  5. Printing the Result:

    println(hough_transform_standard(img))

    This line prints the result of the Hough transform. The Hough transform returns a matrix where the values represent the number of votes for each line in the parameter space. Printing the result shows the distribution of votes for different lines.

In this example, the Hough transform is used to detect the horizontal line in the binary image. The result would show a peak at the corresponding parameter values in the Hough space, indicating the presence of a horizontal line at row 3 in the original image.

Source code in the julia programming language

using ImageFeatures

img = fill(false,5,5)
img[3,:] .= true

println(hough_transform_standard(img))

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