分水嶺分割方法（Watershed Segmentation），是一種基于拓?fù)淅碚摰臄?shù)學(xué)形態(tài)學(xué)的分割方法，其基本思想是把圖像看作是測(cè)地學(xué)上的拓?fù)涞孛玻瑘D像中每一點(diǎn)像素的灰度值表示該點(diǎn)的海拔高度，每一個(gè)局部極小值及其影響區(qū)域稱(chēng)為集水盆，而集水盆的邊界則形成分水嶺。分水嶺的概念和形成可以通過(guò)模擬浸入過(guò)程來(lái)說(shuō)明。在每一個(gè)局部極小值表面，刺穿一個(gè)小孔，然后把整個(gè)模型慢慢浸入水中，隨著浸入的加深，每一個(gè)局部極小值的影響域慢慢向外擴(kuò)展，在兩個(gè)集水盆匯合處構(gòu)筑大壩，即形成分水嶺。
分水嶺的計(jì)算過(guò)程是一個(gè)迭代標(biāo)注過(guò)程。分水嶺比較經(jīng)典的計(jì)算方法是L. Vincent提出的。在該算法中，分水嶺計(jì)算分兩個(gè)步驟，一個(gè)是排序過(guò)程，一個(gè)是淹沒(méi)過(guò)程。首先對(duì)每個(gè)像素的灰度級(jí)進(jìn)行從低到高排序，然后在從低到高實(shí)現(xiàn)淹沒(méi)過(guò)程中，對(duì)每一個(gè)局部極小值在h階高度的影響域采用先進(jìn)先出（FIFO）結(jié)構(gòu)進(jìn)行判斷及標(biāo)注。
分水嶺變換得到的是輸入圖像的集水盆圖像，集水盆之間的邊界點(diǎn)，即為分水嶺。顯然，分水嶺表示的是輸入圖像極大值點(diǎn)。因此，為得到圖像的邊緣信息，通常把梯度圖像作為輸入圖像，即：
grad(f(x,y))=((f(x-1,y)-f(x+1,y))^2 + (f(x,y-1)-f(x,y+1))^2)^0.5
式中，f(x,y)表示原始圖像，grad(.)表示梯度運(yùn)算。
分水嶺算法對(duì)微弱邊緣具有良好的響應(yīng)，圖像中的噪聲、物體表面細(xì)微的灰度變化，都會(huì)產(chǎn)生過(guò)度分割的現(xiàn)象。但同時(shí)應(yīng)當(dāng)看出，分水嶺算法對(duì)微弱邊緣具有良好的響應(yīng)，是得到封閉連續(xù)邊緣的保證的。另外，分水嶺算法所得到的封閉的集水盆，為分析圖像的區(qū)域特征提供了可能。
為消除分水嶺算法產(chǎn)生的過(guò)度分割，通?？梢圆捎脙煞N處理方法，一是利用先驗(yàn)知識(shí)去除無(wú)關(guān)邊緣信息。二是修改梯度函數(shù)使得集水盆只響應(yīng)想要探測(cè)的目標(biāo)。
為降低分水嶺算法產(chǎn)生的過(guò)度分割，通常要對(duì)梯度函數(shù)進(jìn)行修改，一個(gè)簡(jiǎn)單的方法是對(duì)梯度圖像進(jìn)行閾值處理，以消除灰度的微小變化產(chǎn)生的過(guò)度分割。即：
g(x,y)=max(grad(f(x,y)),gθ)
式中，gθ表示閾值。
程序可采用方法：用閾值限制梯度圖像以達(dá)到消除灰度值的微小變化產(chǎn)生的過(guò)度分割，獲得適量的區(qū)域，再對(duì)這些區(qū)域的邊緣點(diǎn)的灰度級(jí)進(jìn)行從低到高排序，然后在從低到高實(shí)現(xiàn)淹沒(méi)的過(guò)程，梯度圖像用Sobel算子計(jì)算獲得。對(duì)梯度圖像進(jìn)行閾值處理時(shí)，選取合適的閾值對(duì)最終分割的圖像有很大影響，因此閾值的選取是圖像分割效果好壞的一個(gè)關(guān)鍵。缺點(diǎn)：實(shí)際圖像中可能含有微弱的邊緣，灰度變化的數(shù)值差別不是特別明顯，選取閾值過(guò)大可能會(huì)消去這些微弱邊緣。
下面用C++實(shí)現(xiàn)分水嶺算法：
#define _USE_MATH_DEFINES #include <cstddef> #include <cstdlib> #include <cstring> #include <climits> #include <cfloat> #include <ctime> #include <cmath> #include <cassert> #include <vector> #include <stack> #include <queue> using namespace std; typedef void GVVoid; typedef bool GVBoolean; typedef char GVChar; typedef unsigned char GVByte; typedef short GVInt16; typedef unsigned short GVUInt16; typedef int GVInt32; typedef unsigned int GVUInt32; typedef long long GVInt64; typedef unsigned long long GVUInt64; typedef float GVFloat32; typedef double GVFloat64; const GVBoolean GV_TRUE = true; const GVBoolean GV_FALSE = false; const GVByte GV_BYTE_MAX = UCHAR_MAX; const GVInt32 GV_INT32_MAX = INT_MAX; const GVInt32 GV_INT32_MIX = INT_MIN; const GVInt64 GV_INT64_MAX = LLONG_MAX; const GVInt64 GV_INT64_MIN = LLONG_MIN; const GVFloat32 GV_FLOAT32_MAX = FLT_MAX; const GVFloat32 GV_FLOAT32_MIN = FLT_MIN; const GVFloat64 GV_FLOAT64_MAX = DBL_MAX; const GVFloat64 GV_FLOAT64_MIN = DBL_MIN; class GVPoint; class GVPoint { public: GVInt32 x; GVInt32 y; public: GVPoint() : x(0), y(0) { } GVPoint(const GVPoint &obj) : x(obj.x), y(obj.y) { } GVPoint(GVInt32 x, GVInt32 y) : x(x), y(y) { } public: GVBoolean operator ==(const GVPoint &right) const { return ((x == right.x) && (y == right.y)); } GVBoolean operator !=(const GVPoint &right) const { return (!(x == right.x) || !(y == right.y)); } }; /* * <Parameter> * <image> image data; * <width> image width; * <height> image height; * <label out> image of labeled watersheds. */ GVVoid gvWatershed( const GVByte *image, GVInt32 width, GVInt32 height, GVInt32 *label) { // Local constants const GVInt32 WSHD = 0; const GVInt32 INIT = -1; const GVInt32 MASK = -2; const GVPoint FICT_PIXEL = GVPoint(~0, ~0); // Image statistics and sorting GVInt32 size = width * height; GVInt32 *image_stat = new GVInt32[GV_BYTE_MAX + 1]; GVInt32 *image_space = new GVInt32[GV_BYTE_MAX + 1]; GVPoint *image_sort = new GVPoint[size]; ::memset(image_stat, 0, sizeof (GVInt32) * (GV_BYTE_MAX + 1)); ::memset(image_space, 0, sizeof (GVInt32) * (GV_BYTE_MAX + 1)); ::memset(image_sort, 0, sizeof (GVPoint) * size); for (GVInt32 i = 0; !(i == size); ++i) { image_stat[image[i]]++; } for (GVInt32 i = 0; !(i == GV_BYTE_MAX); ++i) { image_stat[i + 1] += image_stat[i]; } for (GVInt32 i = 0; !(i == height); ++i) { for (GVInt32 j = 0; !(j == width); ++j) { GVByte space = image[i * width + j]; GVInt32 index = image_stat[space] - (++image_space[space]); image_sort[index].x = j; image_sort[index].y = i; } } for (GVInt32 i = GV_BYTE_MAX; !(i == 0); --i) { image_stat[i] -= image_stat[i - 1]; } // Watershed algorithm GVPoint *head = image_sort; GVInt32 space = 0; GVInt32 *dist = new GVInt32[size]; GVInt32 dist_cnt = 0; GVInt32 label_cnt = 0; std::queue<GVPoint> queue; ::memset(dist, 0, sizeof (GVInt32) * size); ::memset(label, ~0, sizeof (GVInt32) * size); for (GVInt32 h = 0; !(h == (GV_BYTE_MAX + 1)); ++h) { head += space; space = image_stat[h]; for (GVInt32 i = 0; !(i == space); ++i) { GVInt32 index = head[i].y * width + head[i].x; GVInt32 index_l = ((head[i].x - 1) < 0) ? -1 : ((head[i].x - 1) + head[i].y * width); GVInt32 index_r = !((head[i].x + 1) > width) ? -1 : ((head[i].x + 1) + head[i].y * width); GVInt32 index_t = ((head[i].y - 1) < 0) ? -1 : (head[i].x + (head[i].y - 1) * width); GVInt32 index_b = !((head[i].y + 1) > height) ? -1 : (head[i].x + (head[i].y + 1) * width); label[index] = MASK; if ( (!(index_l < 0) && !(label[index_l] < WSHD)) || (!(index_r < 0) && !(label[index_r] < WSHD)) || (!(index_t < 0) && !(label[index_t] < WSHD)) || (!(index_b < 0) && !(label[index_b] < WSHD))) { dist[index] = 1; queue.push(head[i]); } } dist_cnt = 1; queue.push(FICT_PIXEL); while (GV_TRUE) { GVPoint top = queue.front(); GVInt32 index = top.y * width + top.x; GVInt32 index_l = ((top.x - 1) < 0) ? -1 : ((top.x - 1) + top.y * width); GVInt32 index_r = !((top.x + 1) > width) ? -1 : ((top.x + 1) + top.y * width); GVInt32 index_t = ((top.y - 1) < 0) ? -1 : (top.x + (top.y - 1) * width); GVInt32 index_b = !((top.y + 1) > height) ? -1 : (top.x + (top.y + 1) * width); queue.pop(); if (top == FICT_PIXEL) { if (queue.empty()) break; else { ++dist_cnt; queue.push(FICT_PIXEL); top = queue.front(); queue.pop(); } } if (!(index_l < 0)) { if ((dist[index_l] < dist_cnt) && !(label[index_l] < WSHD)) { if (label[index_l] > WSHD) { if ((label[index] == MASK) || (label[index] = WSHD)) label[index] = label[index_l]; else if (!(label[index] == label[index_l])) label[index] = WSHD; } else if (label[index] == MASK) { label[index] = WSHD; } } else if ((label[index_l] == MASK) && (dist[index_l] == 0)) { dist[index_l] = dist_cnt + 1; queue.push(GVPoint(top.x - 1, top.y)); } } if (!(index_r < 0)) { if ((dist[index_r] < dist_cnt) && !(label[index_r] < WSHD)) { if (label[index_r] > WSHD) { if ((label[index] == MASK) || (label[index] = WSHD)) label[index] = label[index_r]; else if (!(label[index] == label[index_r])) label[index] = WSHD; } else if (label[index] == MASK) { label[index] = WSHD; } } else if ((label[index_r] == MASK) && (dist[index_r] == 0)) { dist[index_r] = dist_cnt + 1; queue.push(GVPoint(top.x + 1, top.y)); } } if (!(index_t < 0)) { if ((dist[index_t] < dist_cnt) && !(label[index_t] < WSHD)) { if (label[index_t] > WSHD) { if ((label[index] == MASK) || (label[index] = WSHD)) label[index] = label[index_t]; else if (!(label[index] == label[index_t])) label[index] = WSHD; } else if (label[index] == MASK) { label[index] = WSHD; } } else if ((label[index_t] == MASK) && (dist[index_t] == 0)) { dist[index_t] = dist_cnt + 1; queue.push(GVPoint(top.x, top.y - 1)); } } if (!(index_b < 0)) { if ((dist[index_b] < dist_cnt) && !(label[index_b] < WSHD)) { if (label[index_b] > WSHD) { if ((label[index] == MASK) || (label[index] = WSHD)) label[index] = label[index_b]; else if (!(label[index] == label[index_b])) label[index] = WSHD; } else if (label[index] == MASK) { label[index] = WSHD; } } else if ((label[index_b] == MASK) && (dist[index_b] == 0)) { dist[index_b] = dist_cnt + 1; queue.push(GVPoint(top.x, top.y + 1)); } } } for (GVInt32 i = 0; !(i == space); ++i) { GVInt32 index = head[i].y * width + head[i].x; dist[index] = 0; if (label[index] == MASK) { label_cnt++; label[index] = label_cnt; queue.push(head[i]); while (!queue.empty()) { GVPoint top = queue.front(); GVInt32 index_l = ((top.x - 1) < 0) ? -1 : ((top.x - 1) + top.y * width); GVInt32 index_r = !((top.x + 1) > width) ? -1 : ((top.x + 1) + top.y * width); GVInt32 index_t = ((top.y - 1) < 0) ? -1 : (top.x + (top.y - 1) * width); GVInt32 index_b = !((top.y + 1) > height) ? -1 : (top.x + (top.y + 1) * width); queue.pop(); if (!(index_l < 0) && (label[index_l] == MASK)) { queue.push(GVPoint(top.x - 1, top.y)); label[index_l] = label_cnt; } if (!(index_r < 0) && (label[index_r] == MASK)) { queue.push(GVPoint(top.x + 1, top.y)); label[index_r] = label_cnt; } if (!(index_t < 0) && (label[index_t] == MASK)) { queue.push(GVPoint(top.x, top.y - 1)); label[index_t] = label_cnt; } if (!(index_b < 0) && (label[index_b] == MASK)) { queue.push(GVPoint(top.x, top.y + 1)); label[index_b] = label_cnt; } } } } } // Release resources delete[] image_stat; delete[] image_space; delete[] image_sort; delete[] dist; } 以上就是本文的全部?jī)?nèi)容，希望對(duì)大家的學(xué)習(xí)有所幫助，也希望大家多多支持武林網(wǎng)。
新聞熱點(diǎn)
疑難解答
