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

Published on 12 May 2024 09:40 PM
#Nim

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

Source code in the nim programming language

import lenientops, math
import grayscale_image

const White = 255

func houghTransform*(img: GrayImage; hx = 460; hy = 360): GrayImage =
  assert not img.isNil
  assert hx > 0 and hy > 0
  assert (hy and 1) == 0, "hy argument must be even"

  result = newGrayImage(hx, hy)
  result.fill(White)

  let rMax = hypot(img.w.toFloat, img.h.toFloat)
  let dr = rMax / (hy / 2)
  let dTh = PI / hx

  for y in 0..<img.h:
    for x in 0..<img.w:
      if img[x, y] == White: continue
      for iTh in 0..<hx:
        let th = dTh * iTh
        let r = x * cos(th) + y * sin(th)
        let iry = hy div 2 - (r / dr).toInt
        if result[iTh, iry] > 0:
          result[iTh, iry] = result[iTh, iry] - 1


when isMainModule:
  import nimPNG
  import bitmap

  const Input = "Pentagon.png"
  const Output = "Hough.png"

  let pngImage = loadPNG24(seq[byte], Input).get()
  let grayImage = newGrayImage(pngImage.width, pngImage.height)

  # Convert to grayscale.
  for i in 0..grayImage.pixels.high:
    grayImage.pixels[i] = Luminance(0.2126 * pngImage.data[3 * i] +
                                    0.7152 * pngImage.data[3 * i + 1] +
                                    0.0722 * pngImage.data[3 * i + 2] + 0.5)

  # Apply Hough transform and convert to an RGB image.
  let houghImage = grayImage.houghTransform().toImage()

  # Save into a PNG file.
  # As nimPNG expects a sequence of bytes, not a sequence of colors, we have to make a copy.
  var data = newSeqOfCap[byte](houghImage.pixels.len * 3)
  for color in houghImage.pixels:
    data.add([color.r, color.g, color.b])
  discard savePNG24(Output, data, houghImage.w, houghImage.h)

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