How can measure distance after threshold

Hello,

how can measure the disance (x , y) after threshold (x, y) between the edge of image and the white region.

[Walter Roberson]

A sample image would help.

[weam]

the distance from the right side to any white region , and from bottom to the any white region.

Answer 1

[Image Analyst]

"the distance from the right side to any white region , and from botton to the any white region. "

To find the distance from the right side of the image to any white pixel, you can get that by scanning the image line by line

[rows, columns] = size(binaryImage);
rightEdges = zeros(rows, 1);
for row = 1 : rows
    t = find(binaryImage(row, :), 1, 'last');
    if ~isempty(t)
        rightEdges(row) = t;
    end
end
% Similarly to find the last row in each column, scan column-by-column:
bottomEdges = zeros(1, columns);
for col = 1 : columns
    t = find(binaryImage(:, col), 1, 'last');
    if ~isempty(t)
        bottomEdges(col) = t;
    end    
end
% Find the closest pixel to the right edge of the image
[rightDistance, closestRow] = min(rightEdges)
% Find the closest pixel to the bottom edge of the image
[bottomDistance, closestCol] = min(bottomEdges)

[Walter Roberson]

By the way, the algorithm I posted in my Answer is a vectorized way of finding the last set pixel

Answer 2

[Image Analyst]

Use bwdist on the inverse of the binary image.

help bwdist

 BWDIST Distance transform of binary image.
    D = BWDIST(BW) computes the Euclidean distance transform of the
    binary image BW. For each pixel in BW, the distance transform assigns
    a number that is the distance between that pixel and the nearest
    nonzero pixel of BW. BWDIST uses the Euclidean distance metric by
    default.  BW can have any dimension.  D is the same size as BW.
 
    [D,IDX] = BWDIST(BW) also computes 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
    same size as BW and D. Each element of IDX contains the linear index of
    the nearest nonzero pixel of BW.
 
    [D,IDX] = BWDIST(BW,METHOD) lets you compute an alternate distance
    transform, depending on the value of METHOD.  METHOD can be
    'cityblock', 'chessboard', 'quasi-euclidean', or 'euclidean'.  METHOD
    defaults to 'euclidean' if not specified.  METHOD may be
    abbreviated.
 
    The different methods correspond to different distance metrics.  In
    2-D, the cityblock distance between (x1,y1) and (x2,y2) is abs(x1-x2)
    + abs(y1-y2).  The chessboard distance is max(abs(x1-x2),
    abs(y1-y2)).  The quasi-Euclidean distance is:
 
        abs(x1-x2) + (sqrt(2)-1)*abs(y1-y2),  if abs(x1-x2) > abs(y1-y2)
        (sqrt(2)-1)*abs(x1-x2) + abs(y1-y2),  otherwise
 
    The Euclidean distance is sqrt((x1-x2)^2 + (y1-y2)^2).
 
    Notes
    -----
    BWDIST uses a fast algorithm to compute the true Euclidean distance
    transform.  The other methods are provided primarily for pedagogical
    reasons.
 
    The function BWDIST changed in version 6.4 (R2009b). Previous versions
    of the Image Processing Toolbox used different algorithms for
    computing the Euclidean distance transform and the associated
    closest-pixel map matrix. If you need the same results produced by
    the previous implementation, use the function BWDIST_OLD.
 
    Class support
    -------------
    BW can be numeric or logical, and it must be nonsparse.  D is a
    single matrix with the same size as BW.
    The class of IDX depends on number of elements in the input image,
    and is determined using the following table.
 
        Class         Range
        --------      --------------------------------
        'uint32'      numel(BW) <= 2^32-1
        'uint64'      numel(BW) >= 2^32
 
    Example 1
    ---------
    % Here is a simple example of the Euclidean distance transform:
 
        bw = zeros(5,5);
        bw(2,2) = 1;
        bw(4,4) = 1;
        [D,IDX] = bwdist(bw)
 
    Example 2
    ---------
    % This example compares 2-D distance transforms for the four methods:
 
        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');
        RGB1 = repmat(rescale(D1), [1 1 3]);
        RGB2 = repmat(rescale(D2), [1 1 3]);
        RGB3 = repmat(rescale(D3), [1 1 3]);
        RGB4 = repmat(rescale(D4), [1 1 3]);
        figure
        subplot(2,2,1);
        imshow(RGB1);
        title('Euclidean');
        hold on;
        imcontour(D1);
        subplot(2,2,2);
        imshow(RGB2);
        title('City block');
        hold on;
        imcontour(D2);
        subplot(2,2,3);
        imshow(RGB3);
        title('Chessboard');
        hold on;
        imcontour(D3);
        subplot(2,2,4);
        imshow(RGB4);
        title('Quasi-Euclidean');
        hold on;
        imcontour(D4);
 
    Example 3
    ---------
    % This example compares isosurface plots for the distance transforms of
    % a 3-D image 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');
        figure
        subplot(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');
 
    See also BWDIST_OLD, BWULTERODE, WATERSHED.

    Documentation for bwdist
       doc bwdist

    Other uses of bwdist

       gpuArray/bwdist

[weam]

Thank you so much for your explaining.

Answer 3

[Walter Roberson]

First trim the white border off of the image. Then binarize and take the inverse of the image, so that the black become 1 and the white become 0. Then flipud() and fliplr() the inverse.

Now

vert_profile = fliplr(sum(cumprod(FlippedInverse,1),1));
horz_profile2 = flipud(sum(cumprod(FlippedInverse,2),2));

For any given column K of the cropped image, vert_profile(K) is the number of black rows at the bottom of the image (possibly 0). For any given row K of the cropped image, horz_profile(K) is the number of black columns at the right side of the image (possibly 0)