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F＃，通过对齐直方图来增加图像的对比度

直方图对齐操作（增加对比度）通常用于提高图像质量。在本文的框架中，将考虑直方图的概念，对齐算法的理论以及该算法操作的实际示例。为了方便图像处理，我们将使用OpenCV库。另外，我们将对我们的算法和OpenCV中已经内置的算法的结果进行比较分析。



直方图是函数h（x），该函数返回亮度等于x的像素总数。


半色调图像I的直方图h给出为

H（米）=|（[R，C）|一世（[R，C）=米|


，其中m对应于亮度值的间隔

以下是用于计算直方图的伪代码。


//   H    I.

procedure histogram(I,H);
{
    //     .
    for i := 0 to MaxVal
        H[i] := 0;

    //   .
    for L := 0 to MaxRow
        for P := 0 to MaxCol {
            grayval := I[r,c];
            H[grayval] := H[grayval] + 1;
        };
}

在视觉上，直方图是一个矩形，其宽度等于原始图像中某个点的亮度的最大可能值。对于灰度图像，我们将使用从0到255的点的亮度范围，这意味着直方图的宽度将等于256。直方图的高度可以是任意值，但为清楚起见，我们将使用矩形直方图。


, — 256 ( ), . .


1. h(x)



. — cdf(x) .


, OpenCV , , . , , . F# OpenCVSharp4.


, Visual Studio, . , MacOS, , "runtimes/osx-x64/native/libOpenCvSharpExtern.dylib" , .
Unable to load shared library 'OpenCvSharpExtern' or one of its dependencies


,


open OpenCvSharp
open Microsoft.FSharp.NativeInterop

// mat -   Mat  OpenCV
let getHistogram (mat: Mat) =
    //   
    let hx = Array.zeroCreate<int> 256
    //  
    mat.ForEachAsByte(fun value _ ->
                           let v = int (NativePtr.get value 0)
                           hx.[v] <- hx.[v] + 1)
    //  
    hx

, . X


CdX（X）=H（0）+H（1个）+。。。+H（X）


, X. 1 ( ).


, cdf(x)


let getCdx hx = // hx - 
   //   
   hx |> Array.mapi (fun x _ -> if x > 0 then hx.[0..(x-1)] |> Array.sum else 0)


1 , . ( ), . , , .


2.


2.



, .


:


F（X）=[RØüñd（CdF（X）--CdF米一世ñp一世XË升s--1个⋅255）



cdf(x) — X
cdf_min — ,
pixels —
255 — . 255
round —


F# :


//  cdf_min
let cdxMin = cdx |> Array.filter (fun v -> v > 0) |> Array.min
//      
let totalPixels = src.Rows * src.Cols // src -   Mat   

for y in 0..src.Rows do
    for x in 0..src.Cols do
        //     
        let s = int(src.At<byte>(y, x))
        //     
        let fx = (float(cdx.[s]) - float(cdxMin))/(float(totalPixels - 1))*255.
        //    
        equalizeImage.Circle(x, y, 1, new Scalar(double(fx)))

, . . , OpenCV .


// Learn more about F# at http://fsharp.org
open OpenCvSharp
open Microsoft.FSharp.NativeInterop

//     
let getHistogram (mat: Mat) =
    let hx = Array.zeroCreate<int> 256
    mat.ForEachAsByte(fun value _ ->
                           let v = int (NativePtr.get value 0)
                           hx.[v] <- hx.[v] + 1)
    hx

//      
let getCdx hx =
    hx |> Array.mapi (fun x _ -> if x > 0 then hx.[0..(x-1)] |> Array.sum else 0)

//     
let drawHistogramAndCdx hx cdx (mat: Mat) =
    let histoWidth = 256
    let histoHeight = 256

    //     
    let cdxMax = cdx |> Array.max
    //      ( )
    //    
    let cdxK = float(histoHeight)/float(cdxMax)

    let histMax = hx |> Array.max
    let histK = float(histoHeight)/float(histMax)

    let histMat = new Mat(histoWidth, histoHeight, MatType.CV_8UC4)
    hx
    |> Array.iteri (fun x v ->
                        let histDy = int(float(v)*histK)
                        let cdxDy = int(float(cdx.[x])*cdxK)
                        //   h(x)
                        mat.Line(x, histoHeight-1, x, histoHeight-1-histDy, Scalar.White)
                        //    cdx(x)
                        mat.Circle(x, histoHeight-cdxDy, 1, Scalar.Blue))

[<EntryPoint>]
let main argv =

    let histoWidth = 256
    let histoHeight = 256

    let src = Cv2.ImRead("cat.jpg", ImreadModes.Grayscale)
    let equalizeImage = new Mat(src.Rows, src.Cols, MatType.CV_8UC1)

    // calculate histogram h(x)
    let hx = getHistogram src

    // calculate cdf(x) = h(0) + h(1) + .. + h(x)
    let cdx = getCdx hx

    // draw histogram
    let histMat = new Mat(histoWidth, histoHeight, MatType.CV_8UC4)
    drawHistogramAndCdx hx cdx histMat

    // equalize the histogram
    let cdxMin = cdx |> Array.filter (fun v -> v > 0) |> Array.min
    let totalPixels = src.Rows * src.Cols

    for y in 0..src.Rows do
        for x in 0..src.Cols do
            let s = int(src.At<byte>(y, x))
            let fx = (float(cdx.[s]) - float(cdxMin))/(float(totalPixels - 1))*255.
            //equalizeImage.Set<Scalar>(y, x, new Scalar(double(fx)))
            equalizeImage.Circle(x, y, 1, new Scalar(double(fx)))

    // calculate equalize histogram
    let hx2 = getHistogram equalizeImage
    let cdx2 = getCdx hx2

    let histMat2 = new Mat(histoWidth, histoHeight, MatType.CV_8UC4)
    drawHistogramAndCdx hx2 cdx2 histMat2

    // opencv equalize histogram
    let opencCVImage = new Mat(src.Rows, src.Cols, MatType.CV_8UC1)
    let in1 = InputArray.Create(src)
    let in2 = OutputArray.Create(opencCVImage)

    Cv2.EqualizeHist(in1, in2)

    // get opencv histogram
    let hx3 = getHistogram opencCVImage
    let cdx3 = getCdx hx3

    let histMat3 = new Mat(histoWidth, histoHeight, MatType.CV_8UC4)
    drawHistogramAndCdx hx3 cdx2 histMat3

    // show results
    use w1 = new Window("original image", src)
    use w2 = new Window("original histogram", histMat)

    use w3 = new Window("custom equalize image", equalizeImage)
    use w4 = new Window("custom equalize histogram", histMat2)

    use w5 = new Window("opencv equalize image", opencCVImage)
    use w6 = new Window("opencv equalize histogram", histMat3)

    Cv2.WaitKey() |> ignore

    0 // return an integer exit code


3.


, , OpenCV.


( ), — , — OpenCV.







本文的作者远非原始人，没有提出任何新的建议，而是向公众介绍了另一个有关如何实现直方图对齐算法以及为什么需要它的故事。本文的主要目的不仅是讨论算法，还提供特定的实际示例和源代码，您可以复制和验证自己的代码，还可以进行实验。当然，直方图算法并不是唯一用于过滤图像的算法。但这是其他问题的主题。

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