亮度變換函數(shù)：

1、imadjust(f,[low_in high_in],[low_out

high_out],gamma)

gamma = 1時是線性映射，gamma < 1時高亮度區(qū)域被壓縮，gamma

> 1時低亮度區(qū)域被壓縮。

2、imcomplement(f)

求取圖像的反片

3、對數(shù)變換

用于傅里葉頻譜取值范圍較大，其中高值部分占優(yōu)，從而導致頻譜中低亮度值可視細節(jié)丟失，通過對數(shù)變換可以將動態(tài)范圍降低，從而便于我們處理，公式為：log(1

+ double(f))；

4、對比度拉伸函數(shù)

公式為：g = 1 / (1 + (m ./ (double(f) +

eps)).^E),其中m是均值，E控制斜率，一般取4；

書中將以上變換整理到一個函數(shù)中，代碼如下：

function g = intrans(f, varargin)

%INTRANS Performs intensity (gray-level) transformations.

%?G = INTRANS(F, 'neg')

computes the negative of input image F.

%

%?G = INTRANS(F, 'log', C,

CLASS) computes C*log(1 + F) and

%?multiplies the result by

(positive) constant C. If the last two

%?parameters are omitted, C

defaults to 1. Because the log is used

%?frequently to display Fourier

spectra, parameter CLASS offers the

%?option to specify the class

of the output as 'uint8' or

%?'uint16'. If parameter CLASS

is omitted, the output is of the

%?same class as the

input.

%

%?G = INTRANS(F, 'gamma', GAM)

performs a gamma transformation on

%?the input image using

parameter GAM (a required input).?%

%?G = INTRANS(F, 'stretch', M,

E) computes a contrast-stretching

%?transformation using the

expression 1./(1 + (M./(F +

%?eps)).^E).?Parameter M must be in the range [0, 1].?The

default

%?value for M is

mean2(im2double(F)), and the default value for E

%?is 4.

%

%?For the 'neg', 'gamma', and

'stretch' transformations, double

%?input images whose maximum

value is greater than 1 are scaled

%?first using

MAT2GRAY.?Other images are converted to double

first

%?using

IM2DOUBLE.?For the 'log' transformation, double

images are

%?transformed without being

scaled; other images are converted to

%?double first using

IM2DOUBLE.

%

%?The output is of the same

class as the input, except if a

%?different class is specified

for the 'log' option.

%?Copyright 2002-2004 R. C.

Gonzalez, R. E. Woods, & S. L. Eddins

%?Digital Image Processing

Using MATLAB, Prentice-Hall, 2004

%?$Revision: 1.7

$?$Date: 2003/10/13 00:45:53 $

% Verify the correct number of inputs.

error(nargchk(2, 4, nargin))

% Store the class of the input for use later.

classin = class(f);

% If the input is of class double, and it is outside the

range

% [0, 1], and the specified transformation is not 'log', convert

the

% input to the range [0, 1].

if strcmp(class(f), 'double') & max(f(:))

> 1 & ...

~strcmp(varargin{1}, 'log')

f = mat2gray(f);

else % Convert to double, regardless of class(f).

f = im2double(f);

end

% Determine the type of transformation specified.

method = varargin{1};

% Perform the intensity transformation

specified.?switch method

case 'neg'

g = imcomplement(f);

case 'log'

if length(varargin) ==

1?c = 1;

elseif length(varargin) ==

2?c = varargin{2};

elseif length(varargin) ==

3

c = varargin{2};

classin = varargin{3};

else

error('Incorrect number of inputs for the log option.')

end

g = c*(log(1 +

double(f)));

case 'gamma'

if length(varargin)

< 2

error('Not enough inputs for the gamma option.')

end

gam = varargin{2};

g = imadjust(f, [ ], [ ],

gam);

case 'stretch'

if length(varargin) == 1

% Use defaults.

m = mean2(f);?E =

4.0;?elseif length(varargin) ==

3

m = varargin{2};?E = varargin{3};

else error('Incorrect number

of inputs for the stretch option.')

end

g = 1./(1 + (m./(f +

eps)).^E);

otherwise

error('Unknown enhancement

method.')

end

% Convert to the class of the input image.

g = changeclass(classin, g);

5、直方圖均衡化

histeq(f,nval)，其中nval為輸出圖像的灰度級數(shù)，默認為64；

6、直方圖規(guī)定化

直方圖均衡化可以提高圖像的對比度，但對于圖像灰度值過于集中于0值區(qū)域時，灰度變換函數(shù)是灰度直方圖的累加和的曲線，此時曲線在低值區(qū)域會出現(xiàn)陡峰，因此把灰度級低端過于集中的像素映射到灰度級的高端，并不能提高圖像的對比度。

直方圖規(guī)定化將解決該問題，期望的直方圖應在灰度級有較小的幾種范圍，在保留圖像直方圖大體形狀，其函數(shù)為：

histeq(f，p)

p為期望直方圖，其原理和直方圖均衡化一樣，只不過直方圖均衡化的期望直方圖為等于1的直線，而直方圖規(guī)定化是一個任意的曲線而已，在實際中期望直方圖可以通過雙峰高斯函數(shù)來估計，書中提供雙峰函數(shù)的生成代碼：

function p = twomodegauss(m1, sig1, m2, sig2, A1, A2, k)

%TWOMODEGAUSS Generates a two-mode Gaussian function.

%?P = TWOMODEGAUSS(M1, SIG1,

M2, SIG2, A1, A2, K) generates a

%?two-mode, Gaussian-like

function in the interval [0,1].?P is a

%?256-element vector normalized

so that SUM(P) equals 1.?The mean

%?and standard deviation of the

modes are (M1, SIG1) and (M2,

%?SIG2), respectively. A1 and

A2 are the amplitude values of the

%?two modes.?Since the output is normalized, only the relative

%?values of A1 and A2 are

important.?K is an offset value that

%?raises the "floor" of the

function.?A good set of values to try

%?is M1=0.15, S1=0.05, M2=0.75,

S2=0.05, A1=1, A2=0.07, and

%?K=0.002.

%?Copyright 2002-2004 R. C.

Gonzalez, R. E. Woods, & S. L. Eddins

%?Digital Image Processing

Using MATLAB, Prentice-Hall, 2004

%?$Revision: 1.6

$?$Date: 2003/10/13 00:54:47 $

c1 = A1 * (1 / ((2 * pi) ^ 0.5) * sig1);

k1 = 2 * (sig1 ^ 2);

c2 = A2 * (1 / ((2 * pi) ^ 0.5) * sig2);

k2 = 2 * (sig2 ^ 2);

z?= linspace(0, 1, 256);

p = k + c1 * exp(-((z - m1) .^ 2) ./ k1) + ...

c2 *

exp(-((z - m2) .^ 2) ./ k2);

p = p ./ sum(p(:));

function p = manualhist

%MANUALHIST Generates a two-mode histogram interactively.

%?P = MANUALHIST generates a

two-mode histogram using

%?TWOMODEGAUSS(m1, sig1, m2,

sig2, A1, A2, k).?m1 and m2 are the

%?means of the two modes and

must be in the range [0,1].?sig1 and

%?sig2 are the standard

deviations of the two modes.?A1 and A2 are

%?amplitude values, and k is an

offset value that raised the

%?"floor" of

histogram.?The number of elements in the

histogram

%?vector P is 256 and sum(P) is

normalized to 1.?MANUALHIST

%?repeatedly prompts for the

parameters and plots the resulting

%?histogram until the user

types an 'x' to quit, and then it returns

%?the last histogram

computed.

%

%?A good set of starting values

is: (0.15, 0.05, 0.75, 0.05, 1,

%?0.07,

0.002).

%?Copyright 2002-2004 R. C.

Gonzalez, R. E. Woods, & S. L. Eddins

%?Digital Image Processing

Using MATLAB, Prentice-Hall, 2004

%?$Revision: 1.7

$?$Date: 2003/10/13 00:49:57 $

% Initialize.

repeats = true;

quitnow = 'x';

% Compute a default histogram in case the user quits

before

% estimating at least one histogram.

p = twomodegauss(0.15, 0.05, 0.75, 0.05, 1, 0.07, 0.002);

% Cycle until an x is input.

while repeats?s = input('Enter m1, sig1, m2,

sig2, A1, A2, k OR x to quit:','s');

if s == quitnow

break

end

% Convert the input string to

a vector of numerical values and

% verify the number of

inputs.

v = str2num(s);

if numel(v) ~= 7

disp('Incorrect number of inputs')

continue

end

p = twomodegauss(v(1), v(2),

v(3), v(4), v(5), v(6), v(7));

% Start a new figure and scale

the axes. Specifying only xlim

% leaves ylim on auto.

figure, plot(p)

xlim([0 255])

end

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