圖像增強技術可具體爲時域和頻域。 時域增強往往被應用於提高圖像的對比度且改進其灰度級， 其原理是在灰度映射轉化的基礎上， 對像素進行直接性地處理； 頻域增強的作用是以強化圖像的低、 高頻來達到改善圖像的平滑性和邊緣爲主，其原理是通過傅里葉轉換的方式提升興趣區的頻率分量。
圖像灰度分佈不均的問題對於圖像處理技術而言是一個影響較大的問題， 爲了能解決這個問題， 基於時域增強理論， 採用映射函數當中的非線性函數， 通過轉化後使其像素分佈均勻。
直方圖均衡化方法通過不同的灰度分佈方案使轉變爲灰度值均勻化分佈的圖像，以眼底圖爲例，利用直方圖提取灰度映射曲線，再對其進行轉換，從而提升亮度。但該方法仍有瑕疵，即無法增強其對比度，且在此過程當中，一併將噪聲信號也同時放大了。以 AHE (Adaptive Histogtam Equalization)爲例，該方法將圖像利用網格線切割爲數量衆多的小格子區域， 並對每一個格子進行均衡化處理。但該方法會導致圖像失真， 且其微噪也會因此而放大。 因此， 這裏提出了 對比度受限制自適應直方圖 (Contrast limited Adaptive Histogtam Equalization， CLAHE) ， 即對每一個劃分單元進行對比度的限制處理，這也是該方法與傳統的AHE的不同之處。
CLAHE 通過限制局部直方圖的高度來限制噪聲放大和局部對比度增強。該方法將圖像劃分爲多個子區域； 然後對每個子區域的直方圖進行分類。 再對每個子區域分別進行直方圖均衡化， 最後通過對每個像素進行插值運算來獲得變換後的灰度值，以此實現對比度受限自適應直方圖均衡化圖像增強。
CLAHE 方法原理：
CLAHE 與 AHE 不同的地方是增加對比度限幅，這就可以克服 AHE 的過度放大噪聲的問題；
綜上所述，改變最大的映射函數斜率Smax 及相應的最大直方圖高度Hmax，可獲得不同增強效果的圖像。也就是說限制CDF的斜率就相當於限制Hist的幅度。
因此我們需要對子塊中統計得到的直方圖進行裁剪，使其幅值低於某個上限，當然裁剪掉的部分又不能扔掉，我們還需要將這部分裁剪值均勻地分佈在整個灰度區間上，以保證直方圖總面積不變，如下圖：
可以看到，這時直方圖又會整體上升了一個高度，貌似會超過我們設置的上限。其實在具體實現的時候有很多解決方法，你可以多重複幾次裁剪過程，使得上升的部分變得微不足道，或是用另一種常用的方法：
設裁剪值爲ClipLimit，求直方圖中高於該值的部分的和totalExcess，此時假設將totalExcess均分給所有灰度級， 求出這樣導致的直方圖整體上升的高度L=totalExcess/N，以upper= ClipLimit-L爲界限對直方圖進行如下處理：
(1)若幅值高於ClipLimit，直接置爲ClipLimit；
(2)若幅值處於Upper和ClipLimit之間，將其填補至ClipLimit；
(3)若幅值低於Upper，直接填補L個像素點；
經過上述操作，用來填補的像素點個數通常會略小於totalExcess，也就是還有一些剩餘的像素點沒分出去，這個剩餘來自於(1)(2)兩處。這時我們可以再把這些點均勻地分給那些目前幅值仍然小於ClipLimit的灰度值。
% total number of pixels overflowing clip limit in each bin
totalExcess = sum(max(imgHist - clipLimit,0));
% clip the histogram and redistribute the excess pixels in each bin
avgBinIncr = floor(totalExcess/numBins);
upperLimit = clipLimit - avgBinIncr; % bins larger than this will be
% set to clipLimit
% this loop should speed up the operation by putting multiple pixels
% into the "obvious" places first
for k=1:numBins
if imgHist(k) > clipLimit
imgHist(k) = clipLimit;
else
if imgHist(k) > upperLimit % high bin count
totalExcess = totalExcess - (clipLimit - imgHist(k));
imgHist(k) = clipLimit;
else
totalExcess = totalExcess - avgBinIncr;
imgHist(k) = imgHist(k) + avgBinIncr;
end
end
end
% this loops redistributes the remaining pixels, one pixel at a time
k = 1;
while (totalExcess ~= 0)
%keep increasing the step as fewer and fewer pixels remain for
%the redistribution (spread them evenly)
stepSize = max(floor(numBins/totalExcess),1);
for m=k:stepSize:numBins
if imgHist(m) < clipLimit
imgHist(m) = imgHist(m)+1;
totalExcess = totalExcess - 1; %reduce excess
if totalExcess == 0
break;
end
end
end
k = k+1; %prevent from always placing the pixels in bin #1
if k > numBins % start over if numBins was reached
k = 1;
end
end
CLAHE和AHE中另一個重要的問題：插值。
將圖像進行分塊處理，若每塊中的像素點僅通過該塊中的映射函數進行變換，則會導致最終圖像呈塊狀效應：
爲了解決這個問題，我們需要利用插值運算，也就是每個像素點出的值由它周圍4個子塊的映射函數值進行雙線性插值得到。
上圖中，爲了求藍色像素點處的值，需要利用它周圍四個子塊的映射函數分別做變換得到四個映射值，再對這四個值做雙線性插值即可。
當然對於邊界處的像素點則不是通過四個子塊進行插值，如上圖紅色像素點直接以一個子塊的映射函數做變換，綠色像素則以兩個子塊做映射函數做線性插值。這裏講的邊界處像素是指落在圖像左上角，左下角、右上角，右下角的四個子塊中心像素點圍成的四邊形之外的像素。如下圖，將圖像分爲8x8子塊，邊界像素即落在灰色區域的像素點。
CLAHE算法的源代碼參考:
/*
* ANSI C code from the article
* "Contrast Limited Adaptive Histogram Equalization"
* by Karel Zuiderveld, [email protected]
* in "Graphics Gems IV", Academic Press, 1994
*
*
* These functions implement Contrast Limited Adaptive Histogram Equalization.
* The main routine (CLAHE) expects an input image that is stored contiguously in
* memory; the CLAHE output image overwrites the original input image and has the
* same minimum and maximum values (which must be provided by the user).
* This implementation assumes that the X- and Y image resolutions are an integer
* multiple of the X- and Y sizes of the contextual regions. A check on various other
* error conditions is performed.
*
* #define the symbol BYTE_IMAGE to make this implementation suitable for
* 8-bit images. The maximum number of contextual regions can be redefined
* by changing uiMAX_REG_X and/or uiMAX_REG_Y; the use of more than 256
* contextual regions is not recommended.
*
* The code is ANSI-C and is also C++ compliant.
*
* Author: Karel Zuiderveld, Computer Vision Research Group,
* Utrecht, The Netherlands ([email protected])
*/
#ifdef BYTE_IMAGE
typedef unsigned char kz_pixel_t; /* for 8 bit-per-pixel images */
#define uiNR_OF_GREY (256)
#else
typedef unsigned short kz_pixel_t; /* for 12 bit-per-pixel images (default) */
# define uiNR_OF_GREY (4096)
#endif
/******** Prototype of CLAHE function. Put this in a separate include file. *****/
int CLAHE(kz_pixel_t* pImage, unsigned int uiXRes, unsigned int uiYRes, kz_pixel_t Min,
kz_pixel_t Max, unsigned int uiNrX, unsigned int uiNrY,
unsigned int uiNrBins, float fCliplimit);
/*********************** Local prototypes ************************/
static void ClipHistogram (unsigned long*, unsigned int, unsigned long);
static void MakeHistogram (kz_pixel_t*, unsigned int, unsigned int, unsigned int,
unsigned long*, unsigned int, kz_pixel_t*);
static void MapHistogram (unsigned long*, kz_pixel_t, kz_pixel_t,
unsigned int, unsigned long);
static void MakeLut (kz_pixel_t*, kz_pixel_t, kz_pixel_t, unsigned int);
static void Interpolate (kz_pixel_t*, int, unsigned long*, unsigned long*,
unsigned long*, unsigned long*, unsigned int, unsigned int, kz_pixel_t*);
/************** Start of actual code **************/
#include <stdlib.h> /* To get prototypes of malloc() and free() */
const unsigned int uiMAX_REG_X = 16; /* max. # contextual regions in x-direction */
const unsigned int uiMAX_REG_Y = 16; /* max. # contextual regions in y-direction */
/************************** main function CLAHE ******************/
int CLAHE (kz_pixel_t* pImage, unsigned int uiXRes, unsigned int uiYRes,
kz_pixel_t Min, kz_pixel_t Max, unsigned int uiNrX, unsigned int uiNrY,
unsigned int uiNrBins, float fCliplimit)
/* pImage - Pointer to the input/output image
* uiXRes - Image resolution in the X direction
* uiYRes - Image resolution in the Y direction
* Min - Minimum greyvalue of input image (also becomes minimum of output image)
* Max - Maximum greyvalue of input image (also becomes maximum of output image)
* uiNrX - Number of contextial regions in the X direction (min 2, max uiMAX_REG_X)
* uiNrY - Number of contextial regions in the Y direction (min 2, max uiMAX_REG_Y)
* uiNrBins - Number of greybins for histogram ("dynamic range")
* float fCliplimit - Normalized cliplimit (higher values give more contrast)
* The number of "effective" greylevels in the output image is set by uiNrBins; selecting
* a small value (eg. 128) speeds up processing and still produce an output image of
* good quality. The output image will have the same minimum and maximum value as the input
* image. A clip limit smaller than 1 results in standard (non-contrast limited) AHE.
*/
{
unsigned int uiX, uiY; /* counters */
unsigned int uiXSize, uiYSize, uiSubX, uiSubY; /* size of context. reg. and subimages */
unsigned int uiXL, uiXR, uiYU, uiYB; /* auxiliary variables interpolation routine */
unsigned long ulClipLimit, ulNrPixels;/* clip limit and region pixel count */
kz_pixel_t* pImPointer; /* pointer to image */
kz_pixel_t aLUT[uiNR_OF_GREY]; /* lookup table used for scaling of input image */
unsigned long* pulHist, *pulMapArray; /* pointer to histogram and mappings*/
unsigned long* pulLU, *pulLB, *pulRU, *pulRB; /* auxiliary pointers interpolation */
if (uiNrX > uiMAX_REG_X) return -1; /* # of regions x-direction too large */
if (uiNrY > uiMAX_REG_Y) return -2; /* # of regions y-direction too large */
if (uiXRes % uiNrX) return -3; /* x-resolution no multiple of uiNrX */
if (uiYRes % uiNrY) return -4; /* y-resolution no multiple of uiNrY */
if (Max >= uiNR_OF_GREY) return -5; /* maximum too large */
if (Min >= Max) return -6; /* minimum equal or larger than maximum */
if (uiNrX < 2 || uiNrY < 2) return -7;/* at least 4 contextual regions required */
if (fCliplimit == 1.0) return 0; /* is OK, immediately returns original image. */
if (uiNrBins == 0) uiNrBins = 128; /* default value when not specified */
pulMapArray=(unsigned long *)malloc(sizeof(unsigned long)*uiNrX*uiNrY*uiNrBins);
if (pulMapArray == 0) return -8; /* Not enough memory! (try reducing uiNrBins) */
uiXSize = uiXRes/uiNrX; uiYSize = uiYRes/uiNrY; /* Actual size of contextual regions */
ulNrPixels = (unsigned long)uiXSize * (unsigned long)uiYSize;
if(fCliplimit > 0.0) { /* Calculate actual cliplimit */
ulClipLimit = (unsigned long) (fCliplimit * (uiXSize * uiYSize) / uiNrBins);
ulClipLimit = (ulClipLimit < 1UL) ? 1UL : ulClipLimit;
}
else ulClipLimit = 1UL<<14; /* Large value, do not clip (AHE) */
MakeLut(aLUT, Min, Max, uiNrBins); /* Make lookup table for mapping of greyvalues */
/* Calculate greylevel mappings for each contextual region */
for (uiY = 0, pImPointer = pImage; uiY < uiNrY; uiY++) {
for (uiX = 0; uiX < uiNrX; uiX++, pImPointer += uiXSize) {
pulHist = &pulMapArray[uiNrBins * (uiY * uiNrX + uiX)];
MakeHistogram(pImPointer,uiXRes,uiXSize,uiYSize,pulHist,uiNrBins,aLUT);
ClipHistogram(pulHist, uiNrBins, ulClipLimit);
MapHistogram(pulHist, Min, Max, uiNrBins, ulNrPixels);
}
pImPointer += (uiYSize - 1) * uiXRes; /* skip lines, set pointer */
}
/* Interpolate greylevel mappings to get CLAHE image */
for (pImPointer = pImage, uiY = 0; uiY <= uiNrY; uiY++) {
if (uiY == 0) { /* special case: top row */
uiSubY = uiYSize >> 1; uiYU = 0; uiYB = 0;
}
else {
if (uiY == uiNrY) { /* special case: bottom row */
uiSubY = (uiYSize+1) >> 1; uiYU = uiNrY-1; uiYB = uiYU;
}
else { /* default values */
uiSubY = uiYSize; uiYU = uiY - 1; uiYB = uiYU + 1;
}
}
for (uiX = 0; uiX <= uiNrX; uiX++) {
if (uiX == 0) { /* special case: left column */
uiSubX = uiXSize >> 1; uiXL = 0; uiXR = 0;
}
else {
if (uiX == uiNrX) { /* special case: right column */
uiSubX = (uiXSize+1) >> 1; uiXL = uiNrX - 1; uiXR = uiXL;
}
else { /* default values */
uiSubX = uiXSize; uiXL = uiX - 1; uiXR = uiXL + 1;
}
}
pulLU = &pulMapArray[uiNrBins * (uiYU * uiNrX + uiXL)];
pulRU = &pulMapArray[uiNrBins * (uiYU * uiNrX + uiXR)];
pulLB = &pulMapArray[uiNrBins * (uiYB * uiNrX + uiXL)];
pulRB = &pulMapArray[uiNrBins * (uiYB * uiNrX + uiXR)];
Interpolate(pImPointer,uiXRes,pulLU,pulRU,pulLB,pulRB,uiSubX,uiSubY,aLUT);
pImPointer += uiSubX; /* set pointer on next matrix */
}
pImPointer += (uiSubY - 1) * uiXRes;
}
free(pulMapArray); /* free space for histograms */
return 0; /* return status OK */
}
void ClipHistogram (unsigned long* pulHistogram, unsigned int
uiNrGreylevels, unsigned long ulClipLimit)
/* This function performs clipping of the histogram and redistribution of bins.
* The histogram is clipped and the number of excess pixels is counted. Afterwards
* the excess pixels are equally redistributed across the whole histogram (providing
* the bin count is smaller than the cliplimit).
*/
{
unsigned long* pulBinPointer, *pulEndPointer, *pulHisto;
unsigned long ulNrExcess, ulUpper, ulBinIncr, ulStepSize, i;
long lBinExcess;
ulNrExcess = 0; pulBinPointer = pulHistogram;
for (i = 0; i < uiNrGreylevels; i++) { /* calculate total number of excess pixels */
lBinExcess = (long) pulBinPointer[i] - (long) ulClipLimit;
if (lBinExcess > 0) ulNrExcess += lBinExcess; /* excess in current bin */
};
/* Second part: clip histogram and redistribute excess pixels in each bin */
ulBinIncr = ulNrExcess / uiNrGreylevels; /* average binincrement */
ulUpper = ulClipLimit - ulBinIncr; /* Bins larger than ulUpper set to cliplimit */
for (i = 0; i < uiNrGreylevels; i++) {
if (pulHistogram[i] > ulClipLimit) pulHistogram[i] = ulClipLimit; /* clip bin */
else {
if (pulHistogram[i] > ulUpper) { /* high bin count */
ulNrExcess -= pulHistogram[i] - ulUpper; pulHistogram[i]=ulClipLimit;
}
else { /* low bin count */
ulNrExcess -= ulBinIncr; pulHistogram[i] += ulBinIncr;
}
}
}
while (ulNrExcess) { /* Redistribute remaining excess */
pulEndPointer = &pulHistogram[uiNrGreylevels]; pulHisto = pulHistogram;
while (ulNrExcess && pulHisto < pulEndPointer) {
ulStepSize = uiNrGreylevels / ulNrExcess;
if (ulStepSize < 1) ulStepSize = 1; /* stepsize at least 1 */
for (pulBinPointer=pulHisto; pulBinPointer < pulEndPointer && ulNrExcess;
pulBinPointer += ulStepSize) {
if (*pulBinPointer < ulClipLimit) {
(*pulBinPointer)++; ulNrExcess--; /* reduce excess */
}
}
pulHisto++; /* restart redistributing on other bin location */
}
}
}
void MakeHistogram (kz_pixel_t* pImage, unsigned int uiXRes,
unsigned int uiSizeX, unsigned int uiSizeY,
unsigned long* pulHistogram,
unsigned int uiNrGreylevels, kz_pixel_t* pLookupTable)
/* This function classifies the greylevels present in the array image into
* a greylevel histogram. The pLookupTable specifies the relationship
* between the greyvalue of the pixel (typically between 0 and 4095) and
* the corresponding bin in the histogram (usually containing only 128 bins).
*/
{
kz_pixel_t* pImagePointer;
unsigned int i;
for (i = 0; i < uiNrGreylevels; i++) pulHistogram[i] = 0L; /* clear histogram */
for (i = 0; i < uiSizeY; i++) {
pImagePointer = &pImage[uiSizeX];
while (pImage < pImagePointer) pulHistogram[pLookupTable[*pImage++]]++;
pImagePointer += uiXRes;
pImage = &pImagePointer[-(int)uiSizeX]; /* go to bdeginning of next row */
}
}
void MapHistogram (unsigned long* pulHistogram, kz_pixel_t Min, kz_pixel_t Max,
unsigned int uiNrGreylevels, unsigned long ulNrOfPixels)
/* This function calculates the equalized lookup table (mapping) by
* cumulating the input histogram. Note: lookup table is rescaled in range [Min..Max].
*/
{
unsigned int i; unsigned long ulSum = 0;
const float fScale = ((float)(Max - Min)) / ulNrOfPixels;
const unsigned long ulMin = (unsigned long) Min;
for (i = 0; i < uiNrGreylevels; i++) {
ulSum += pulHistogram[i]; pulHistogram[i]=(unsigned long)(ulMin+ulSum*fScale);
if (pulHistogram[i] > Max) pulHistogram[i] = Max;
}
}
void MakeLut (kz_pixel_t * pLUT, kz_pixel_t Min, kz_pixel_t Max, unsigned int uiNrBins)
/* To speed up histogram clipping, the input image [Min,Max] is scaled down to
* [0,uiNrBins-1]. This function calculates the LUT.
*/
{
int i;
const kz_pixel_t BinSize = (kz_pixel_t) (1 + (Max - Min) / uiNrBins);
for (i = Min; i <= Max; i++) pLUT[i] = (i - Min) / BinSize;
}
void Interpolate (kz_pixel_t * pImage, int uiXRes, unsigned long * pulMapLU,
unsigned long * pulMapRU, unsigned long * pulMapLB, unsigned long * pulMapRB,
unsigned int uiXSize, unsigned int uiYSize, kz_pixel_t * pLUT)
/* pImage - pointer to input/output image
* uiXRes - resolution of image in x-direction
* pulMap* - mappings of greylevels from histograms
* uiXSize - uiXSize of image submatrix
* uiYSize - uiYSize of image submatrix
* pLUT - lookup table containing mapping greyvalues to bins
* This function calculates the new greylevel assignments of pixels within a submatrix
* of the image with size uiXSize and uiYSize. This is done by a bilinear interpolation
* between four different mappings in order to eliminate boundary artifacts.
* It uses a division; since division is often an expensive operation, I added code to
* perform a logical shift instead when feasible.
*/
{
const unsigned int uiIncr = uiXRes-uiXSize; /* Pointer increment after processing row */
kz_pixel_t GreyValue; unsigned int uiNum = uiXSize*uiYSize; /* Normalization factor */
unsigned int uiXCoef, uiYCoef, uiXInvCoef, uiYInvCoef, uiShift = 0;
if (uiNum & (uiNum - 1)) /* If uiNum is not a power of two, use division */
for (uiYCoef = 0, uiYInvCoef = uiYSize; uiYCoef < uiYSize;
uiYCoef++, uiYInvCoef--,pImage+=uiIncr) {
for (uiXCoef = 0, uiXInvCoef = uiXSize; uiXCoef < uiXSize;
uiXCoef++, uiXInvCoef--) {
GreyValue = pLUT[*pImage]; /* get histogram bin value */
*pImage++ = (kz_pixel_t ) ((uiYInvCoef * (uiXInvCoef*pulMapLU[GreyValue]
+ uiXCoef * pulMapRU[GreyValue])
+ uiYCoef * (uiXInvCoef * pulMapLB[GreyValue]
+ uiXCoef * pulMapRB[GreyValue])) / uiNum);
}
}
else { /* avoid the division and use a right shift instead */
while (uiNum >>= 1) uiShift++; /* Calculate 2log of uiNum */
for (uiYCoef = 0, uiYInvCoef = uiYSize; uiYCoef < uiYSize;
uiYCoef++, uiYInvCoef--,pImage+=uiIncr) {
for (uiXCoef = 0, uiXInvCoef = uiXSize; uiXCoef < uiXSize;
uiXCoef++, uiXInvCoef--) {
GreyValue = pLUT[*pImage]; /* get histogram bin value */
*pImage++ = (kz_pixel_t)((uiYInvCoef* (uiXInvCoef * pulMapLU[GreyValue]
+ uiXCoef * pulMapRU[GreyValue])
+ uiYCoef * (uiXInvCoef * pulMapLB[GreyValue]
+ uiXCoef * pulMapRB[GreyValue])) >> uiShift);
}
}
}
}
參考：
[1] https://wenku.baidu.com/view/03c54c02760bf78a6529647d27284b73f342368b.html
[2] https://blog.csdn.net/u010839382/article/details/49584181
[3] https://en.wikipedia.org/wiki/Adaptive_histogram_equalization