Step by Step solution about How to resolve the algorithm Voronoi diagram step by step in the Julia programming language

Voronoi Diagrams

Overview:

Voronoi diagrams are mathematical structures that divide a plane into regions based on distances to a set of specified points (called centroids). Each region in a Voronoi diagram contains all points that are closer to its centroid than to any other centroid. This source code implements Voronoi diagrams in the Julia programming language.

Function: voronoi

The voronoi function generates a Voronoi diagram from scratch. It takes three parameters:

• w: Width of the desired image
• h: Height of the desired image
• n_centroids: Number of centroids to use

Algorithm:

1. Generate random centroids within the specified dimensions.
2. Calculate the distance from each pixel in the image to each centroid.
3. For each pixel, find the nearest centroid and assign the pixel's color to the color of that centroid.

Function: voronoi_img!

The voronoi_img! function modifies an existing image to create a Voronoi diagram:

• img: The input image to be modified
• n_centroids: Number of centroids to use

Algorithm:

1. Generate random centroids within the dimensions of the input image.
2. Calculate the distance from each pixel in the image to each centroid.
3. For each pixel, find the nearest centroid and replace the pixel's color with the color of that centroid.

Example Usage:

The code includes two examples of usage:

1. Creating a Voronoi diagram from scratch using voronoi(800, 600, 200) and displaying the resulting image.
2. Modifying the "mandrill" test image using voronoi_img!(img, 300).

using Images
function voronoi(w, h, n_centroids)
    dist = (point,vector) -> sqrt.((point[1].-vector[:,1]).^2 .+ (point[2].-vector[:,2]).^2)
    dots = [rand(1:h, n_centroids) rand(1:w, n_centroids) rand(RGB{N0f8}, n_centroids)]
    img  = zeros(RGB{N0f8}, h, w)
    for x in 1:h, y in 1:w
        distances = dist([x,y],dots) # distance
        nn = findmin(distances)[2]
        img[x,y]  = dots[nn,:][3]
    end
    return img
end
img = voronoi(800, 600, 200)


using TestImages, Images
function voronoi_img!(img, n_centroids)
    n,m = size(img)
    w   = minimum([n,m])
    dist = (point,vector) -> sqrt.((point[1].-vector[:,1]).^2 .+ (point[2].-vector[:,2]).^2)
    dots = [rand(1:n, n_centroids) rand(1:m, n_centroids)]
    c = []
    for i in 1:size(dots,1)
        p = dots[i,:]
        append!(c, [img[p[1],p[2]]])
    end
    dots = [dots c]
    
    for x in 1:n, y in 1:m
        distances = dist([x,y],dots) # distance
        nn = findmin(distances)[2]
        img[x,y]  = dots[nn,:][3]
    end
end
img = testimage("mandrill")
voronoi_img!(img, 300)