Как сделать хитрый детектор краев в Python, например функцию edge() Matlab

Я хочу использовать функцию edge() Matlab внутри Python:

mask = double(edge(mask,'canny',threshold));

Я пытаюсь найти функцию, эквивалентную функции edge() Matlab в Python. Я попробовал функцию cv2.Canny() в Python, но она отличается от функции Matlab (вы можете прочитать объяснение различий здесь: https://dsp.stackexchange.com/questions/4716/differences-between-opencv-canny-and-matlab-canny). Я попробовал предложение на этом форуме сначала размыть изображение с помощью размытия по Гауссу, но результат все еще отличается от результата Matlab.

Итак, я нашел некоторый код детектора краев Matlab, и я пытаюсь превратить этот код во встроенную функцию edge(), подобную той, что используется в Matlab. Коды, которые я нашел, это:

Первый код:

clear all;
clc;



%Input image
img = imread ('gambar.jpg');
%Show input image
figure, imshow(img);
img = rgb2gray(img);
img = double (img);

%Value for Thresholding
T_Low = 0.2;
T_High = 0.5;

%Gaussian Filter Coefficient
B = [2, 4, 5, 4, 2; 4, 9, 12, 9, 4;5, 12, 15, 12, 5;4, 9, 12, 9, 4;2, 4, 5, 4, 2 ];
B = 1/159.* B;

%Convolution of image by Gaussian Coefficient
A=conv2(img, B, 'same');

%Filter for horizontal and vertical direction
KGx = [-1, 0, 1; -2, 0, 2; -1, 0, 1];
KGy = [1, 2, 1; 0, 0, 0; -1, -2, -1];

%Convolution by image by horizontal and vertical filter
Filtered_X = conv2(A, KGx, 'same');
Filtered_Y = conv2(A, KGy, 'same');

%Calculate directions/orientations
arah = atan2 (Filtered_Y, Filtered_X);
arah = arah*180/pi;

pan=size(A,1);
leb=size(A,2);

%Adjustment for negative directions, making all directions positive
for i=1:pan
    for j=1:leb
        if (arah(i,j)<0) 
            arah(i,j)=360+arah(i,j);
        end;
    end;
end;

arah2=zeros(pan, leb);

%Adjusting directions to nearest 0, 45, 90, or 135 degree
for i = 1  : pan
    for j = 1 : leb
        if ((arah(i, j) >= 0 ) && (arah(i, j) < 22.5) || (arah(i, j) >= 157.5) && (arah(i, j) < 202.5) || (arah(i, j) >= 337.5) && (arah(i, j) <= 360))
            arah2(i, j) = 0;
        elseif ((arah(i, j) >= 22.5) && (arah(i, j) < 67.5) || (arah(i, j) >= 202.5) && (arah(i, j) < 247.5))
            arah2(i, j) = 45;
        elseif ((arah(i, j) >= 67.5 && arah(i, j) < 112.5) || (arah(i, j) >= 247.5 && arah(i, j) < 292.5))
            arah2(i, j) = 90;
        elseif ((arah(i, j) >= 112.5 && arah(i, j) < 157.5) || (arah(i, j) >= 292.5 && arah(i, j) < 337.5))
            arah2(i, j) = 135;
        end;
    end;
end;

figure, imagesc(arah2); colorbar;

%Calculate magnitude
magnitude = (Filtered_X.^2) + (Filtered_Y.^2);
magnitude2 = sqrt(magnitude);

BW = zeros (pan, leb);

%Non-Maximum Supression
for i=2:pan-1
    for j=2:leb-1
        if (arah2(i,j)==0)
            BW(i,j) = (magnitude2(i,j) == max([magnitude2(i,j), magnitude2(i,j+1), magnitude2(i,j-1)]));
        elseif (arah2(i,j)==45)
            BW(i,j) = (magnitude2(i,j) == max([magnitude2(i,j), magnitude2(i+1,j-1), magnitude2(i-1,j+1)]));
        elseif (arah2(i,j)==90)
            BW(i,j) = (magnitude2(i,j) == max([magnitude2(i,j), magnitude2(i+1,j), magnitude2(i-1,j)]));
        elseif (arah2(i,j)==135)
            BW(i,j) = (magnitude2(i,j) == max([magnitude2(i,j), magnitude2(i+1,j+1), magnitude2(i-1,j-1)]));
        end;
    end;
end;

BW = BW.*magnitude2;
figure, imshow(BW);

%Hysteresis Thresholding
T_Low = T_Low * max(max(BW));
T_High = T_High * max(max(BW));

T_res = zeros (pan, leb);

for i = 1  : pan
    for j = 1 : leb
        if (BW(i, j) < T_Low)
            T_res(i, j) = 0;
        elseif (BW(i, j) > T_High)
            T_res(i, j) = 1;
        %Using 8-connected components
        elseif ( BW(i+1,j)>T_High || BW(i-1,j)>T_High || BW(i,j+1)>T_High || BW(i,j-1)>T_High || BW(i-1, j-1)>T_High || BW(i-1, j+1)>T_High || BW(i+1, j+1)>T_High || BW(i+1, j-1)>T_High)
            T_res(i,j) = 1;
        end;
    end;
end;

edge_final = uint8(T_res.*255);
%Show final edge detection result
figure, imshow(edge_final);

Из: https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/63294/versions/9/previews/MaxPol%20Package/demo%20examples/forward%20signal%20and%20imaging%20problems/Canny%20edge%20detection/canny_edge.m/index.html?access_key=

Второй код:

function [eout, dx, dy] = canny_edge(image_scan, smoothing_kernel, derivative_kernel)

thresh = [0.2 0.5];
sigma = sqrt(2);
thinning = true;
H = [];
kx = 1;
ky = 1;

[m,n] = size(image_scan);
e = false(m,n);
% Magic numbers
PercentOfPixelsNotEdges = .7; % Used for selecting thresholds
ThresholdRatio = .4;          % Low thresh is this fraction of the high.


dx = imfilter(image_scan, smoothing_kernel', 'conv', 'replicate');
dx = imfilter(dx, derivative_kernel, 'conv', 'replicate');

% Compute smoothed numerical gradient of image I along y (vertical)
% direction. GY corresponds to dG/dy, where G is the Gaussian Smoothed
% version of image I.
dy = imfilter(image_scan, smoothing_kernel, 'conv', 'replicate');
dy  = imfilter(dy, derivative_kernel', 'conv', 'replicate');

% Calculate Magnitude of Gradient
magGrad = hypot(dx, dy);

% Normalize for threshold selection
magmax = max(magGrad(:));
if magmax > 0
    magGrad = magGrad / magmax;
end

% Determine Hysteresis Thresholds
[lowThresh, highThresh] = selectThresholds(thresh, magGrad, PercentOfPixelsNotEdges, ThresholdRatio, mfilename);

% Perform Non-Maximum Suppression Thining and Hysteresis Thresholding of Edge
% Strength
eout = thinAndThreshold(e, dx, dy, magGrad, lowThresh, highThresh);
thresh = [lowThresh highThresh];


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : selectThresholds
%
function [lowThresh, highThresh] = selectThresholds(thresh, magGrad, PercentOfPixelsNotEdges, ThresholdRatio, ~)

[m,n] = size(magGrad);

% Select the thresholds
if isempty(thresh)
    counts=imhist(magGrad, 64);
    highThresh = find(cumsum(counts) > PercentOfPixelsNotEdges*m*n,...
        1,'first') / 64;
    lowThresh = ThresholdRatio*highThresh;
elseif length(thresh)==1
    highThresh = thresh;
    if thresh>=1
        error(message('images:edge:thresholdMustBeLessThanOne'))
    end
    lowThresh = ThresholdRatio*thresh;
elseif length(thresh)==2
    lowThresh = thresh(1);
    highThresh = thresh(2);
    if (lowThresh >= highThresh) || (highThresh >= 1)
        error(message('images:edge:thresholdOutOfRange'))
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : thinAndThreshold
%
function H = thinAndThreshold(E, dx, dy, magGrad, lowThresh, highThresh)

% Perform Non-Maximum Suppression Thining and Hysteresis Thresholding of Edge
% Strength

% We will accrue indices which specify ON pixels in strong edgemap
% The array e will become the weak edge map.
idxStrong = [];
for dir = 1:4
    idxLocalMax = cannyFindLocalMaxima(dir,dx,dy,magGrad);
    idxWeak = idxLocalMax(magGrad(idxLocalMax) > lowThresh);
    E(idxWeak)=1;
    idxStrong = [idxStrong; idxWeak(magGrad(idxWeak) > highThresh)]; %#ok<AGROW>
end

[m,n] = size(E);

if ~isempty(idxStrong) % result is all zeros if idxStrong is empty
    rstrong = rem(idxStrong-1, m)+1;
    cstrong = floor((idxStrong-1)/m)+1;
    H = bwselect(E, cstrong, rstrong, 8);
else
    H = zeros(m, n);
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : cannyFindLocalMaxima
%
function idxLocalMax = cannyFindLocalMaxima(direction,ix,iy,mag)
%
% This sub-function helps with the non-maximum suppression in the Canny
% edge detector.  The input parameters are:
%
%   direction - the index of which direction the gradient is pointing,
%               read from the diagram below. direction is 1, 2, 3, or 4.
%   ix        - input image filtered by derivative of gaussian along x
%   iy        - input image filtered by derivative of gaussian along y
%   mag       - the gradient magnitude image
%
%    there are 4 cases:
%
%                         The X marks the pixel in question, and each
%         3     2         of the quadrants for the gradient vector
%       O----0----0       fall into two cases, divided by the 45
%     4 |         | 1     degree line.  In one case the gradient
%       |         |       vector is more horizontal, and in the other
%       O    X    O       it is more vertical.  There are eight
%       |         |       divisions, but for the non-maximum suppression
%    (1)|         |(4)    we are only worried about 4 of them since we
%       O----O----O       use symmetric points about the center pixel.
%        (2)   (3)


[m,n] = size(mag);

% Find the indices of all points whose gradient (specified by the
% vector (ix,iy)) is going in the direction we're looking at.

switch direction
    case 1
        idx = find((iy<=0 & ix>-iy)  | (iy>=0 & ix<-iy));
    case 2
        idx = find((ix>0 & -iy>=ix)  | (ix<0 & -iy<=ix));
    case 3
        idx = find((ix<=0 & ix>iy) | (ix>=0 & ix<iy));
    case 4
        idx = find((iy<0 & ix<=iy) | (iy>0 & ix>=iy));
end

% Exclude the exterior pixels
if ~isempty(idx)
    v = mod(idx,m);
    extIdx = (v==1 | v==0 | idx<=m | (idx>(n-1)*m));
    idx(extIdx) = [];
end

ixv = ix(idx);
iyv = iy(idx);
gradmag = mag(idx);

% Do the linear interpolations for the interior pixels
switch direction
    case 1
        d = abs(iyv./ixv);
        gradmag1 = mag(idx+m).*(1-d) + mag(idx+m-1).*d;
        gradmag2 = mag(idx-m).*(1-d) + mag(idx-m+1).*d;
    case 2
        d = abs(ixv./iyv);
        gradmag1 = mag(idx-1).*(1-d) + mag(idx+m-1).*d;
        gradmag2 = mag(idx+1).*(1-d) + mag(idx-m+1).*d;
    case 3
        d = abs(ixv./iyv);
        gradmag1 = mag(idx-1).*(1-d) + mag(idx-m-1).*d;
        gradmag2 = mag(idx+1).*(1-d) + mag(idx+m+1).*d;
    case 4
        d = abs(iyv./ixv);
        gradmag1 = mag(idx-m).*(1-d) + mag(idx-m-1).*d;
        gradmag2 = mag(idx+m).*(1-d) + mag(idx+m+1).*d;
end
idxLocalMax = idx(gradmag>=gradmag1 & gradmag>=gradmag2);

Из: https://www.mathworks.com/matlabcentral/fileexchange/46859-canny-edge-detection

Который я пытаюсь преобразовать в эту встроенную функцию edge() matlab:

function [eout,thresh,gv_45,gh_135] = edge(varargin)
args = matlab.images.internal.stringToChar(varargin);
[a,method,thresh,sigma,thinning,H,kx,ky] = parse_inputs(args{:});

% Check that the user specified a valid number of output arguments
if ~any(strcmp(method,{'sobel','roberts','prewitt'})) && (nargout>2)
    error(message('images:edge:tooManyOutputs'))
end

% Transform to a double precision intensity image if necessary
isPrewittOrSobel = strcmp(method,'sobel') || strcmp(method,'prewitt');
if ~isPrewittOrSobel && ~isfloat(a) && ~strcmp(method,'approxcanny')
    a = im2single(a);
end


[m,n] = size(a);

if strcmp(method,'canny')
    % Magic numbers
    PercentOfPixelsNotEdges = .7; % Used for selecting thresholds
    ThresholdRatio = .4;          % Low thresh is this fraction of the high.

    % Calculate gradients using a derivative of Gaussian filter
    [dx, dy] = smoothGradient(a, sigma);

    % Calculate Magnitude of Gradient
    magGrad = hypot(dx, dy);

    % Normalize for threshold selection
    magmax = max(magGrad(:));
    if magmax > 0
        magGrad = magGrad / magmax;
    end

    % Determine Hysteresis Thresholds
    [lowThresh, highThresh] = selectThresholds(thresh, magGrad, PercentOfPixelsNotEdges, ThresholdRatio, mfilename);

    % Perform Non-Maximum Suppression Thining and Hysteresis Thresholding of Edge
    % Strength
    e = thinAndThreshold(dx, dy, magGrad, lowThresh, highThresh);
    thresh = [lowThresh highThresh];

elseif strcmp(method,'approxcanny')
    e = computeapproxcanny(a, thresh);

elseif strcmp(method,'canny_old')
    % Magic numbers
    GaussianDieOff = .0001;
    PercentOfPixelsNotEdges = .7; % Used for selecting thresholds
    ThresholdRatio = .4;          % Low thresh is this fraction of the high.

    % Design the filters - a gaussian and its derivative

    pw = 1:30; % possible widths
    ssq = sigma^2;
    width = find(exp(-(pw.*pw)/(2*ssq))>GaussianDieOff,1,'last');
    if isempty(width)
        width = 1;  % the user entered a really small sigma
    end

    t = (-width:width);
    gau = exp(-(t.*t)/(2*ssq))/(2*pi*ssq);     % the gaussian 1D filter

    % Find the directional derivative of 2D Gaussian (along X-axis)
    % Since the result is symmetric along X, we can get the derivative along
    % Y-axis simply by transposing the result for X direction.
    [x,y]=meshgrid(-width:width,-width:width);
    dgau2D=-x.*exp(-(x.*x+y.*y)/(2*ssq))/(pi*ssq);

    % Convolve the filters with the image in each direction
    % The canny edge detector first requires convolution with
    % 2D Gaussian, and then with the derivative of a Gaussian.
    % Since Gaussian filter is separable, for smoothing, we can use
    % two 1D convolutions in order to achieve the effect of convolving
    % with 2D Gaussian.  We convolve along rows and then columns.

    %smooth the image out
    aSmooth=imfilter(a,gau,'conv','replicate');   % run the filter across rows
    aSmooth=imfilter(aSmooth,gau','conv','replicate'); % and then across columns

    %apply directional derivatives
    ax = imfilter(aSmooth, dgau2D, 'conv','replicate');
    ay = imfilter(aSmooth, dgau2D', 'conv','replicate');

    mag = sqrt((ax.*ax) + (ay.*ay));
    magmax = max(mag(:));
    if magmax>0
        mag = mag / magmax;   % normalize
    end

    % Select the thresholds
    if isempty(thresh)
        counts=imhist(mag, 64);
        highThresh = find(cumsum(counts) > PercentOfPixelsNotEdges*m*n,...
            1,'first') / 64;
        lowThresh = ThresholdRatio*highThresh;
        thresh = [lowThresh highThresh];
    elseif length(thresh)==1
        highThresh = thresh;
        if thresh>=1
            error(message('images:edge:singleThresholdOutOfRange'))
        end
        lowThresh = ThresholdRatio*thresh;
        thresh = [lowThresh highThresh];
    elseif length(thresh)==2
        lowThresh = thresh(1);
        highThresh = thresh(2);
        if (lowThresh >= highThresh) || (highThresh >= 1)
            error(message('images:edge:thresholdOutOfRange'))
        end
    end

    % The next step is to do the non-maximum suppression. We will accrue
    % indices which specify ON pixels in strong edgemap The array e will become
    % the weak edge map.
    e = cannyFindLocalMaxima(ax,ay,mag,lowThresh);

    if ~isempty(e)
        [rstrong,cstrong] = find(mag>highThresh & e);

        if ~isempty(rstrong) % result is all zeros if idxStrong is empty
            e = bwselect(e, cstrong, rstrong, 8);
            e = bwmorph(e, 'thin', 1); % Thin double (or triple) pixel wide contours
        end
    end

elseif any(strcmp(method, {'log','zerocross'}))
    % The output edge map:
    e = false(m,n);

    rr = 2:m-1; cc=2:n-1;

    % We don't use image blocks here
    if isempty(H)
        fsize = ceil(sigma*3) * 2 + 1;  % choose an odd fsize > 6*sigma;
        op = fspecial('log',fsize,sigma);
    else
        op = H;
    end

    op = op - sum(op(:))/numel(op); % make the op to sum to zero
    b = imfilter(a,op,'replicate');

    if isempty(thresh)
        thresh = 0.75 * sum(abs(b(:)),'double') / numel(b);
    end

    % Look for the zero crossings:  +-, -+ and their transposes
    % We arbitrarily choose the edge to be the negative point
    [rx,cx] = find( b(rr,cc) < 0 & b(rr,cc+1) > 0 ...
        & abs( b(rr,cc)-b(rr,cc+1) ) > thresh );   % [- +]
    e((rx+1) + cx*m) = 1;
    [rx,cx] = find( b(rr,cc-1) > 0 & b(rr,cc) < 0 ...
        & abs( b(rr,cc-1)-b(rr,cc) ) > thresh );   % [+ -]
    e((rx+1) + cx*m) = 1;
    [rx,cx] = find( b(rr,cc) < 0 & b(rr+1,cc) > 0 ...
        & abs( b(rr,cc)-b(rr+1,cc) ) > thresh);   % [- +]'
    e((rx+1) + cx*m) = 1;
    [rx,cx] = find( b(rr-1,cc) > 0 & b(rr,cc) < 0 ...
        & abs( b(rr-1,cc)-b(rr,cc) ) > thresh);   % [+ -]'
    e((rx+1) + cx*m) = 1;

    % Most likely this covers all of the cases.   Just check to see if there
    % are any points where the LoG was precisely zero:
    [rz,cz] = find( b(rr,cc)==0 );
    if ~isempty(rz)
        % Look for the zero crossings: +0-, -0+ and their transposes
        % The edge lies on the Zero point
        zero = (rz+1) + cz*m;   % Linear index for zero points
        zz = (b(zero-1) < 0 & b(zero+1) > 0 ...
            & abs( b(zero-1)-b(zero+1) ) > 2*thresh);     % [- 0 +]'
        e(zero(zz)) = 1;
        zz = (b(zero-1) > 0 & b(zero+1) < 0 ...
            & abs( b(zero-1)-b(zero+1) ) > 2*thresh);     % [+ 0 -]'
        e(zero(zz)) = 1;
        zz = (b(zero-m) < 0 & b(zero+m) > 0 ...
            & abs( b(zero-m)-b(zero+m) ) > 2*thresh);     % [- 0 +]
        e(zero(zz)) = 1;
        zz = (b(zero-m) > 0 & b(zero+m) < 0 ...
            & abs( b(zero-m)-b(zero+m) ) > 2*thresh);     % [+ 0 -]
        e(zero(zz)) = 1;
    end

else  % one of the easy methods (roberts,sobel,prewitt)

    if isPrewittOrSobel
        isSobel = strcmp(method, 'sobel');
        scale = 4; % for calculating the automatic threshold
        offset = [0 0 0 0]; % offsets used in the computation of the threshold

        [bx, by, b] = edgesobelprewittmex(a, isSobel, kx, ky); 

    elseif strcmp(method, 'roberts')
        x_mask = [1 0; 0 -1]/2; % Roberts approximation to diagonal derivative
        y_mask = [0 1;-1  0]/2;

        scale = 6;
        offset = [-1 1 1 -1];

        % compute the gradient in x and y direction
        bx = imfilter(a,x_mask,'replicate');
        by = imfilter(a,y_mask,'replicate');

        % compute the magnitude
        b = kx*bx.*bx + ky*by.*by;

    else
        error(message('images:edge:invalidEdgeDetectionMethod', method))
    end

    if (nargout > 2) % if gradients are requested
        gv_45  = bx;
        gh_135 = by;
    end

    % Determine the threshold; see page 514 of
    % "Digital Imaging Processing" by William K. Pratt
    if isempty(thresh) % Determine cutoff based on RMS estimate of noise
        % Mean of the magnitude squared image is a
        % value that's roughly proportional to SNR
        cutoff = scale * sum(b(:),'double') / numel(b);
        thresh = sqrt(cutoff);
    else
        % Use relative tolerance specified by the user
        cutoff = (thresh).^2;
    end

    if thinning
        e = computeedge(b,bx,by,kx,ky,int8(offset),100*eps,cutoff);
    else
        e = b > cutoff;
    end

end

if nargout==0
    imshow(e);
else
    eout = e;
end

if isempty(a)
    if nargout==2
        if nargin == 2
            if strcmp(method,'canny')
                thresh = nan(1,2);
            else
                thresh = nan(1);
            end
        end
    end    
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : parse_inputs
%
function [I,Method,Thresh,Sigma,Thinning,H,kx,ky] = parse_inputs(varargin)
% OUTPUTS:
%   I      Image Data
%   Method Edge detection method
%   Thresh Threshold value
%   Sigma  standard deviation of Gaussian
%   H      Filter for Zero-crossing detection
%   kx,ky  From Directionality vector

narginchk(1,5)

I = varargin{1};

validateattributes(I,{'numeric','logical'},{'real','nonsparse','2d'},mfilename,'I',1);

% Defaults
Method    = 'sobel';
Direction = 'both';
Thinning  = true;

methods    = {'canny','approxcanny','canny_old','prewitt','sobel','marr-hildreth','log','roberts','zerocross'};
directions = {'both','horizontal','vertical'};
options    = {'thinning','nothinning'};

% Now parse the nargin-1 remaining input arguments

% First get the strings - we do this because the interpretation of the
% rest of the arguments will depend on the method.
nonstr = [];   % ordered indices of non-string arguments
for i = 2:nargin
    if ischar(varargin{i})
        str = lower(varargin{i});
        j = find(strcmp(str,methods));
        k = find(strcmp(str,directions));
        l = find(strcmp(str,options));
        if ~isempty(j)
            Method = methods{j(1)};
            if strcmp(Method,'marr-hildreth')
                error(message('images:removed:syntax','EDGE(I,''marr-hildreth'',...)','EDGE(I,''log'',...)')) 
            end
        elseif ~isempty(k)
            Direction = directions{k(1)};
        elseif ~isempty(l)
            if strcmp(options{l(1)},'thinning')
                Thinning = true;
            else
                Thinning = false;
            end
        else
            error(message('images:edge:invalidInputString', varargin{ i }))
        end
    else
        nonstr = [nonstr i]; %#ok<AGROW>
    end
end

% Now get the rest of the arguments
[Thresh,Sigma,H,kx,ky] = images.internal.parseNonStringInputsEdge(varargin,Method,Direction,nonstr);
validateattributes(Thresh,{'numeric'},{'real'},mfilename,'thresh',3);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : smoothGradient
%
function [GX, GY] = smoothGradient(I, sigma)

% Create an even-length 1-D separable Derivative of Gaussian filter

% Determine filter length
filterExtent = ceil(4*sigma);
x = -filterExtent:filterExtent;

% Create 1-D Gaussian Kernel
c = 1/(sqrt(2*pi)*sigma);
gaussKernel = c * exp(-(x.^2)/(2*sigma^2));

% Normalize to ensure kernel sums to one
gaussKernel = gaussKernel/sum(gaussKernel);

% Create 1-D Derivative of Gaussian Kernel
derivGaussKernel = gradient(gaussKernel);

% Normalize to ensure kernel sums to zero
negVals = derivGaussKernel < 0;
posVals = derivGaussKernel > 0;
derivGaussKernel(posVals) = derivGaussKernel(posVals)/sum(derivGaussKernel(posVals));
derivGaussKernel(negVals) = derivGaussKernel(negVals)/abs(sum(derivGaussKernel(negVals)));

% Compute smoothed numerical gradient of image I along x (horizontal)
% direction. GX corresponds to dG/dx, where G is the Gaussian Smoothed
% version of image I.
GX = imfilter(I, gaussKernel', 'conv', 'replicate');
GX = imfilter(GX, derivGaussKernel, 'conv', 'replicate');

% Compute smoothed numerical gradient of image I along y (vertical)
% direction. GY corresponds to dG/dy, where G is the Gaussian Smoothed
% version of image I.
GY = imfilter(I, gaussKernel, 'conv', 'replicate');
GY  = imfilter(GY, derivGaussKernel', 'conv', 'replicate');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : selectThresholds
%
function [lowThresh, highThresh] = selectThresholds(thresh, magGrad, PercentOfPixelsNotEdges, ThresholdRatio, ~)

[m,n] = size(magGrad);

% Select the thresholds
if isempty(thresh)
    counts=imhist(magGrad, 64);
    highThresh = find(cumsum(counts) > PercentOfPixelsNotEdges*m*n,...
        1,'first') / 64;
    lowThresh = ThresholdRatio*highThresh;
elseif length(thresh)==1
    highThresh = thresh;
    if thresh>=1
        error(message('images:edge:singleThresholdOutOfRange'))
    end
    lowThresh = ThresholdRatio*thresh;
elseif length(thresh)==2
    lowThresh = thresh(1);
    highThresh = thresh(2);
    if (lowThresh >= highThresh) || (highThresh >= 1)
        error(message('images:edge:thresholdOutOfRange'))
    end
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : thinAndThreshold
%
function H = thinAndThreshold(dx, dy, magGrad, lowThresh, highThresh)
% Perform Non-Maximum Suppression Thining and Hysteresis Thresholding of
% Edge Strength

% We will accrue indices which specify ON pixels in strong edgemap
% The array e will become the weak edge map.

E = cannyFindLocalMaxima(dx,dy,magGrad,lowThresh);

if ~isempty(E)
    [rstrong,cstrong] = find(magGrad>highThresh & E);

    if ~isempty(rstrong) % result is all zeros if idxStrong is empty
        H = bwselect(E, cstrong, rstrong, 8);
    else
        H = false(size(E));
    end
else
    H = false(size(E));
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Local Function : computeapproxcanny
%
function e = computeapproxcanny(a, thresh)
    a = im2uint8(a);
    if isempty(a)
        e = logical([]);
    else
        if isempty(thresh)
            e = images.internal.ocvcanny(a);
        else
            if numel(thresh) == 1
                e = images.internal.ocvcanny(a, 0.4*thresh, thresh);
            else
                e = images.internal.ocvcanny(a, thresh(2), thresh(1));
            end
        end
        e = logical(e);
    end

(вы можете увидеть код, набрав «редактировать край» без кавычек внутри Matlab)

Есть ли у кого-нибудь какие-либо предложения или код Python для детектора краев, который совпадает с функцией Matlab edge()? Любое предложение или ответ будет очень полезным. Спасибо.