[數字圖像處理]（一）彩色圖像轉灰度圖像的三種方式與效果分析

圖像處理（一）

彩色圖片轉灰度圖片

---

三種實現方式

• 最大值法

  \(imMax = max( im(i,j,1),im(i,j,2),im(i,j,3) )\)

• 平均法

  \(imEva = \frac{im(i,j,1)}{3} + \frac{im(i,j,2)}{3} + \frac{im(i,j,3)}{3}\)

• 加權平均值法

  \(imKeyEva = 0.2989\times im(i,j,1) + 0.5870\times im(i,j,2) + 0.1140\times im(i,j,3)\)

matlba實現

clc;
close all;
clear all;

%   相對路徑讀入圖片（和代碼在同一文件夾下）
im = imread('p2.jpg');
%---查看圖片，檢測是否成功讀入
%   對顯示的圖片進行排版
subplot(2,3,4);
imshow(im);
%   對圖片進行命名
title('原圖');
[col,row,color] = size(im);%col為圖片的行數，row為圖片的列數，color對於彩色圖片一般為3，每層對應RGB
%利用matlab自帶的函數進行 rgb_to_gray;
im_matlab = rgb2gray(im);
subplot(2,3,1);
imshow(im_matlab);
title('matlab自帶rgb2gray');
%--------------------------------------------------------
%---用最大值法
%   創建一個全為1的矩陣，長寬等同於原圖的
im_max = ones(col,row);

for i = 1:1:col
    for j = 1:1:row
        im_max(i,j) = max( im(i,j,:)  );
    end
end
%   將矩陣變為8byte無符號整型變量（不然無法顯示圖片）
%   ！！！最好在計算操作結束后再變化，不然會有精度問題！！！！！
im_max = uint8(im_max);
subplot(2,3,2);
imshow(im_max);
title('最大值法');
%--------------------------------------------------------
%    平均值法 
im_eva = ones(col,row);

for i = 1:1:col
    for j = 1:1:row
        im_eva(i,j) = im(i,j,1)/3 + im(i,j,2)/3 + im(i,j,3)/3 ;
        %   兩種的結果其實一樣，但是如果先轉換為uint8就會出現精度問題
        %sum1 = im(i,j,1)/3 + im(i,j,2)/3 + im(i,j,3)/3
        %sum2 = ( im(i,j,1) + im(i,j,2)+ im(i,j,3) )/3;
        %fprintf( " %.4f  %.4f \n",sum1 ,sum2 ) ;
    end
end
im_eva = uint8(im_max);
subplot(2,3,3);
imshow(im_eva);
title('平均值法');
%--------------------------------------------------------
%    加權平均法（rgb2gray所使用的權值）
im_keyeva = ones(col,row);
%   加權算法先轉換為uint8計算效果更好
im_keyeva = uint8(im_max);
for i = 1:1:col
    for j = 1:1:row
        im_keyeva(i,j) = 0.2989*im(i,j,1) + 0.5870*im(i,j,2) + 0.1140*im(i,j,3) ;
    end
end

subplot(2,3,5);
imshow(im_keyeva);
title('加權平均法');

附matlab——rgb2gray源碼

function I = rgb2gray(X)
%RGB2GRAY Convert RGB image or colormap to grayscale.
%   RGB2GRAY converts RGB images to grayscale by eliminating the
%   hue and saturation information while retaining the
%   luminance.
%
%   I = RGB2GRAY(RGB) converts the truecolor image RGB to the
%   grayscale intensity image I.
%
%   NEWMAP = RGB2GRAY(MAP) returns a grayscale colormap
%   equivalent to MAP.
%
%   Class Support
%   -------------  
%   If the input is an RGB image, it can be of any numeric type. The output
%   image I has the same class as the input image. If the input is a
%   colormap, the input and output colormaps are both of class double.
%
%   Notes
%   -----
%   RGB2GRAY converts RGB values to grayscale values by forming a weighted 
%   sum of the R, G, and B components:
%
%   0.2989 * R + 0.5870 * G + 0.1140 * B
%
%   The coefficients used to calculate grayscale values in RGB2GRAY are 
%   identical to those used to calculate luminance (E'y) in 
%   Rec.ITU-R BT.601-7 after rounding to 3 decimal places.
%
%   Rec.ITU-R BT.601-7 calculates E'y using the following formula: 
%
%   0.299 * R + 0.587 * G + 0.114 * B 
%
%   Example
%   -------
%   I = imread('example.tif');
%
%   J = rgb2gray(I);
%   figure, imshow(I), figure, imshow(J);
%
%   indImage = load('clown');
%   gmap = rgb2gray(indImage.map);
%   figure, imshow(indImage.X,indImage.map), figure, imshow(indImage.X,gmap);
%
%   See also RGB2IND, RGB2LIGHTNESS.

%   Copyright 1992-2020 The MathWorks, Inc.

narginchk(1,1);

isRGB = parse_inputs(X);
if isRGB
    I = matlab.images.internal.rgb2gray(X);
else
    % Color map
    % Calculate transformation matrix
    T    = inv([1.0 0.956 0.621; 1.0 -0.272 -0.647; 1.0 -1.106 1.703]);
    coef = T(1,:);
    I = X * coef';
    I = min(max(I,0),1);
    I = repmat(I, [1 3]);
end

%--------------------------------------------------------------------------
function is3D = parse_inputs(X)

is3D = (ndims(X) == 3);
if is3D
    % RGB
    if (size(X,3) ~= 3)
        error(message('MATLAB:images:rgb2gray:invalidInputSizeRGB'))
    end
    % RGB can be single, double, int8, uint8,
    % int16, uint16, int32, uint32, int64 or uint64
    validateattributes(X, {'numeric'}, {}, mfilename, 'RGB');
elseif ismatrix(X)
    % MAP
    if (size(X,2) ~= 3 || size(X,1) < 1)
        error(message('MATLAB:images:rgb2gray:invalidSizeForColormap'))
    end
    % MAP must be double
    if ~isa(X,'double')
        error(message('MATLAB:images:rgb2gray:notAValidColormap'))
    end
else
    error(message('MATLAB:images:rgb2gray:invalidInputSize'))
end

總結

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通過上面的代碼結合實際的測試，果然，matlab自帶的rgb2gray也就是加權平均的方法，對光線明暗的處理是最好的。