灰度阀值变换及二值化

?0x?Tf?x????255x?T当图像的像素点的灰度大于T的时候，设置这个点为全黑，要不然为全白。这样可以只选择我们感兴趣的领域。

im2bw(I,level); %阈值法从灰度图、RGB图创建二值图。level为人工设定阈值(threshold value)，范围为[0 ,1]

最大类间方差法（OTSU算法）

最大类间方差法是由日本学者大津(Nobuyuki Otsu)于1979年提出的,是一种自适应的阈值确定的方法,又叫大律法,简称OTSU。它是按图像的灰度特性,将图像分成背景和目标2部分。背景和目标之间的类间方差越大,说明构成图像的2部分的差别越大,当部分目标错分为背景或部分背景错分为目标都会导致2部分差别变小。因此,使类间方差最大的分割意味着错分概率最小。

在Matlab中， graythresh函数使用最大类间方差法获得图像的阈值。

(注意标点‘‘要换一下)

I = imread(‘beauty_yellowflowers.jpg’); thresh= graythresh(I);%自适应设置阀值 bw1 = im2bw(I, thresh);

bw2 = im2bw(I, 130/255);%手工设置阀值 subplot(1,3,1);imshow(I);title(‘original’)

subplot(1,3,2);imshow(bw1);title(‘autoset_thresh’); subplot(1,3,3);imshow(bw2); title(‘thresh=130’);

最小分类错误全局二值化算法 (kittlerMet算法)

函数源代码：

function imagBW = kittlerMet(imag)

% KITTLERMET binarizes a gray scale image 'imag' into a binary image % Input:

% imag: the gray scale image, with black foreground(0), and white % background(255). % Output:

% imagBW: the binary image of the gray scale image 'imag', with kittler's % minimum error thresholding algorithm.

% Reference:

% J. Kittler and J. Illingworth. Minimum Error Thresholding. Pattern % Recognition. 1986. 19(1):41-47

MAXD = 100000; imag = imag(:,:,1);

[counts, x] = imhist(imag); % counts are the histogram. x is the intensity level. GradeI = length(x); % the resolusion of the intensity. i.e. 256 for uint8. J_t = zeros(GradeI, 1); % criterion function

prob = counts ./ sum(counts); % Probability distribution meanT = x' * prob; % Total mean level of the picture % Initialization

w0 = prob(1); % Probability of the first class

miuK = 0; % First-order cumulative moments of the histogram up to the kth level. J_t(1) = MAXD; n = GradeI-1; for i = 1 : n

w0 = w0 + prob(i+1);

miuK = miuK + i * prob(i+1); % first-order cumulative moment if (w0 < eps) || (w0 > 1-eps) J_t(i+1) = MAXD; % T = i else

miu1 = miuK / w0;

miu2 = (meanT-miuK) / (1-w0);

var1 = (((0 : i)'-miu1).^2)' * prob(1 : i+1); var1 = var1 / w0; % variance

var2 = (((i+1 : n)'-miu2).^2)' * prob(i+2 : n+1); var2 = var2 / (1-w0);

if var1 > eps && var2 > eps % in case of var1=0 or var2 =0

J_t(i+1) = 1+w0 * log(var1)+(1-w0) * log(var2)-2*w0*log(w0)-2*(1-w0)*log(1-w0); else

J_t(i+1) = MAXD; end end end

minJ = min(J_t);

index = find(J_t == minJ); th = mean(index); th = (th-1)/n

imagBW = im2bw(imag, th);

% figure, imshow(imagBW), title('kittler binary');

MATLAB程序：

I = imread('beauty_yellowflowers.jpg'); imagSW = kittlerMet(I);%Kittler 算法 bw1 = im2bw(I, 130/255);%手工设置阀值