一、簡介

1 最小誤差法原理
最小誤差閾值分割法是根據影象中背景和目標畫素的概率分佈密度來實現的，其思想是找到一個閾值，並根據該閾值進行劃分，計算出目標點誤分為背景的概率和背景點誤分為目標點的概率，得出總的誤差劃分概率。當總的誤差劃分概率最小時，便得到所需要的最佳閾值。




2 最小誤差法實現步驟

根據圖可得最小誤差閾值法的演算法步驟：
步驟1：假設目標和背景灰度值得密度為，。計算混合概率密度。
步驟2：選定閾值T，計算總的誤差概率，對進行求導。
步驟3：根據準則函式，計算使其最小時的T，作為最佳閾值。

二、原始碼

function varargout = MainForm(varargin)
% MAINFORM MATLAB code for MainForm.fig
%      MAINFORM, by itself, creates a new MAINFORM or raises the existing
%      singleton*.
%
%      H = MAINFORM returns the handle to a new MAINFORM or the handle to
%      the existing singleton*.
%
%      MAINFORM('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in MAINFORM.M with the given input arguments.
%
%      MAINFORM('Property','Value',...) creates a new MAINFORM or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before MainForm_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to MainForm_OpeningFcn via varargin.
%
%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one
%      instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help MainForm

% Last Modified by GUIDE v2.5 02-May-2021 08:10:18

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
    'gui_Singleton',  gui_Singleton, ...
    'gui_OpeningFcn', @MainForm_OpeningFcn, ...
    'gui_OutputFcn',  @MainForm_OutputFcn, ...
    'gui_LayoutFcn',  [] , ...
    'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT

function InitAxes(handles)
clc;
axes(handles.axes1); cla reset;
set(handles.axes1, 'XTick', [], 'YTick', [], ...
    'XTickLabel', '', 'YTickLabel', '', 'Color', [0.7020 0.7804 1.0000], 'Box', 'On');
axes(handles.axes2); cla reset;
set(handles.axes2, 'XTick', [], 'YTick', [], ...
    'XTickLabel', '', 'YTickLabel', '', 'Color', [0.7020 0.7804 1.0000], 'Box', 'On');

function filePath = OpenFile(imgfilePath)
% 開啟檔案
% 輸出引數：
% filePath——檔案路徑

if nargin < 1
    imgfilePath = fullfile(pwd, 'images/test.jpg');
end
[filename, pathname, ~] = uigetfile( ...
    { '*.jpg','All jpg Files';...
    '*.png','All png Files';...
    '*.*',  '所有檔案 (*.*)'}, ...
    '選擇檔案', ...
    'MultiSelect', 'off', ...
    imgfilePath);
filePath = 0;
if isequal(filename, 0) || isequal(pathname, 0)
    return;
end
filePath = fullfile(pathname, filename);

% --- Executes just before MainForm is made visible.
function MainForm_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to MainForm (see VARARGIN)

% Choose default command line output for MainForm
handles.output = hObject;
InitAxes(handles);
handles.I = 0;
handles.J = 0;
handles.bw_direct = 0;
handles.bw_poly = 0;
handles.bw__kittler = 0;
handles.bw_temp = 0;
% Update handles structure
guidata(hObject, handles);

% UIWAIT makes MainForm wait for user response (see UIRESUME)
% uiwait(handles.figure1);


% --- Outputs from this function are returned to the command line.
function varargout = MainForm_OutputFcn(hObject, eventdata, handles)
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;


% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
filePath = OpenFile();
if isequal(filePath, 0)
    return;
end
Img = imread(filePath);
% 灰度化
if ndims(Img) == 3
    I = rgb2gray(Img);
else
    I = Img;
end
axes(handles.axes1);
imshow(I, []);
title('原影象');
handles.I = I;
guidata(hObject, handles);

% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton2 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if isequal(handles.I, 0)
    return;
end
% 直接二值化
bw_direct = im2bw(handles.I, graythresh(handles.I));
axes(handles.axes2);
imshow(bw_direct, []);
title('直接二值化分割');
handles.bw_direct = bw_direct;
guidata(hObject, handles);

% --- Executes on button press in pushbutton3.
function pushbutton3_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton3 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if isequal(handles.bw_direct, 0)
    return;
end
% 圈選胃區域空氣

bw_poly = roipoly(handles.bw_direct, c, r);
axes(handles.axes2);
imshow(handles.I, []);
hold on;
plot(c, r, 'r-', 'LineWidth', 2);
hold off;
title('胃區域空氣選擇');
handles.bw_poly = bw_poly;
guidata(hObject, handles);

% --- Executes on button press in pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton4 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if isequal(handles.bw_poly, 0)
    return;
end
% 影象歸一化
IE = mat2gray(handles.I);
% 對比度增強
IE = imadjust(IE, [0.532 0.72], [0 1]);
IE = im2uint8(mat2gray(IE));
I = im2uint8(mat2gray(handles.I));
% 顯示
axes(handles.axes2);
imshow(IE, []);
title('影象增強');
figure;
subplot(2, 2, 1); imshow(I); title('原影象');
subplot(2, 2, 2); imshow(IE); title('增強影象');
subplot(2, 2, 3); imhist(I); title('原影象直方圖');
subplot(2, 2, 4); imhist(IE); title('增強影象直方圖');
JE = IE;
JE(handles.bw_poly) = 255;
handles.JE = JE;
guidata(hObject, handles);

% --- Executes on button press in pushbutton5.
function pushbutton5_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton5 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if isequal(handles.JE, 0)
    return;
end
J = handles.JE;
% 直方圖統計
[counts, gray_style] = imhist(J);
% 亮度級別
gray_level = length(gray_style);
% 計算各灰度概率
gray_probability  = counts ./ sum(counts);
% 統計畫素均值
gray_mean = gray_style' * gray_probability;
% 初始化

gray_vector(1) = realmax;
ks = gray_level-1;
for k = 1 : ks
    % 迭代計算
    w = w + gray_probability(k+1);
    mean_k = mean_k + k * gray_probability(k+1);
    % 判斷是否收斂
    if (w < eps) || (w > 1-eps)
        gray_vector(k+1) = realmax;
    else
        % 計算均值
        mean_k1 = mean_k / w;
        mean_k2 = (gray_mean-mean_k) / (1-w);
        % 計算方差
        var_k1 = (((0 : k)'-mean_k1).^2)' * gray_probability(1 : k+1);
        var_k1 = var_k1 / w;
        var_k2 = (((k+1 : ks)'-mean_k2).^2)' * gray_probability(k+2 : ks+1);
        var_k2 = var_k2 / (1-w);
        % 計算目標函式
        if var_k1 > eps && var_k2 > eps
            
        else
            gray_vector(k+1) = realmax;
        end
    end
end
 

三、執行結果

四、備註

版本：2014a
完整程式碼或代寫加1564658423