距离变换 matlab实现 opencv实现

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距离变换将一幅二值图像（特征点为0，非特征点为1）变换为一幅灰度图像，灰度图像每一点的像素值为二值图像上非零像素到最近的0像素的距离。

Syntax

D = bwdist(BW) [D,IDX] = bwdist(BW) [D,IDX] = bwdist(BW,method)

Description

D = bwdist(BW) computesthe Euclidean distance transform of the binary imageBW.For each pixel inBW, the distance transform assignsa number that is the distance between that pixel and the nearest nonzeropixel ofBW.bwdist uses theEuclidean distance metric by default. BW can haveany dimension.D is the same size asBW.

[D,IDX] = bwdist(BW) alsocomputes the closest-pixel map in the form of an index array,IDX.(The closest-pixel map is also called the feature map, feature transform,or nearest-neighbor transform.)IDX has the samesize as BW and D. Each elementofIDX contains the linear index of the nearestnonzero pixel ofBW.

[D,IDX] = bwdist(BW,method) computesthe distance transform, wheremethod specifiesan alternate distance metric.method cantake any of the following values. Themethod stringcan be abbreviated.

Method

Description

'chessboard'

In2-D, the chessboard distance between (x₁,y₁) and (x₂,y₂)is max(│x₁ –x₂│,│y₁ –y₂│).

'cityblock'

In2-D, the cityblock distance between (x₁,y₁) and (x₂,y₂)is │x₁ –x₂│+ │y₁ –y₂│.

'euclidean'

In2-D, the Euclidean distance between (x₁,y₁) and (x₂,y₂)is

This is the default method.

'quasi-euclidean'

In2-D, the quasi-Euclidean distance between (x₁,y₁)and (x₂,y₂) is

Class Support

BW can be numeric or logical, and it mustbe nonsparse. D is a single matrix with the samesize asBW. The class ofIDX dependson the number of elements in the input image, and is determined usingthe following table.

ClassRange'uint32'numel(BW) <= 2³² −1'uint64'numel(BW) >= 2³²

Examples

Compute the Euclidean distance transform.

bw = zeros(5,5); bw(2,2) = 1; bw(4,4) = 1bw =     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0[D,IDX] = bwdist(bw)D =    1.4142    1.0000    1.4142    2.2361    3.1623    1.0000         0    1.0000    2.0000    2.2361    1.4142    1.0000    1.4142    1.0000    1.4142    2.2361    2.0000    1.0000         0    1.0000    3.1623    2.2361    1.4142    1.0000    1.4142IDX =     7     7     7     7     7     7     7     7     7    19     7     7     7    19    19     7     7    19    19    19     7    19    19    19    19

In the nearest-neighbor matrix IDX the values 7 and 19 representthe position of the nonzero elements using linear matrix indexing.If a pixel contains a 7, its closest nonzero neighbor is at linearposition 7.

Compare the 2-D distance transforms for each of the supporteddistance methods. In the figure, note how the quasi-Euclidean distancetransform best approximates the circular shape achieved by the Euclideandistance method.

bw = zeros(200,200); bw(50,50) = 1; bw(50,150) = 1;bw(150,100) = 1;D1 = bwdist(bw,'euclidean');D2 = bwdist(bw,'cityblock');D3 = bwdist(bw,'chessboard');D4 = bwdist(bw,'quasi-euclidean');figuresubplot(2,2,1), subimage(mat2gray(D1)), title('Euclidean')hold on, imcontour(D1)subplot(2,2,2), subimage(mat2gray(D2)), title('City block')hold on, imcontour(D2)subplot(2,2,3), subimage(mat2gray(D3)), title('Chessboard')hold on, imcontour(D3)subplot(2,2,4), subimage(mat2gray(D4)), title('Quasi-Euclidean')hold on, imcontour(D4)

Compare isosurface plots for the distance transforms of a 3-Dimage containing a single nonzero pixel in the center.

bw = zeros(50,50,50); bw(25,25,25) = 1;D1 = bwdist(bw);D2 = bwdist(bw,'cityblock');D3 = bwdist(bw,'chessboard');D4 = bwdist(bw,'quasi-euclidean');figuresubplot(2,2,1), isosurface(D1,15), axis equal, view(3)camlight, lighting gouraud, title('Euclidean')subplot(2,2,2), isosurface(D2,15), axis equal, view(3)camlight, lighting gouraud, title('City block')subplot(2,2,3), isosurface(D3,15), axis equal, view(3)camlight, lighting gouraud, title('Chessboard')subplot(2,2,4), isosurface(D4,15), axis equal, view(3)camlight, lighting gouraud, title('Quasi-Euclidean')