# graydiffweight

Calculate weights for image pixels based on grayscale intensity difference

## Description

W = graydiffweight(I,refGrayVal) computes the pixel weight for each pixel in the grayscale image I. The weight is the absolute value of the difference between the intensity of the pixel and the reference grayscale intensity specified by the scalar refGrayVal. Pick a reference grayscale intensity value that is representative of the object you want to segment. The weights are returned in the array W, which is the same size as input image I.

The weight of a pixel is inversely related to the absolute value of the grayscale intensity difference at the pixel location. If the difference is small (intensity value close to refGrayVal), the weight value is large. If the difference is large (intensity value very different from refGrayVal), the weight value is small.

W = graydiffweight(I,mask) computes the pixel weights, where the reference grayscale intensity value is the average of the intensity values of all the pixels in I that are marked as logical true in mask. Using the average of several pixels to calculate the reference grayscale intensity value can be more effective than using a single reference intensity value, as in the previous syntax.

W = graydiffweight(I,C,R) computes the pixel weights, where the reference grayscale intensity value is the average of the intensity values of the pixel locations specified by the vectors C and R. C and R contain the column and row indices of the pixel locations that must be valid pixel indices in I.

W = graydiffweight(V,C,R,P) computes the weights for each voxel in the volume V, specified by the vectors C, R, and P. C, R, and P contain the column, row, and plane indices of the voxel locations that must be valid voxel indices in V.

example

W = graydiffweight(___, Name,Value) returns the weight array W using name-value pairs to control aspects of weight computation.

Note

For information on how to use the graydiffweight function with the imsegfmm function for image and volume segmentation, see the More About section.

## Examples

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This example segments an object in an image using Fast Marching Method using grayscale intensity difference weights calculated from the intensity values at the seed locations.

imshow(I)
title('Original Image')

Specify row and column index of pixels for use a reference grayscale intensity value.

seedpointR = 159;
seedpointC = 67;

Calculate the grayscale intensity difference weight array for the image and display it. The example does log-scaling of W for better visualization.

W = graydiffweight(I, seedpointC, seedpointR,'GrayDifferenceCutoff',25);
figure, imshow(log(W),[])

Segment the image using the grayscale intensity difference weight array. Specify the same seed point vectors you used to create the weight array.

thresh = 0.01;
BW = imsegfmm(W, seedpointC, seedpointR, thresh);
figure, imshow(BW)
title('Segmented Image')

## Input Arguments

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Grayscale image, specified as a 2-D numeric matrix.

Data Types: single | double | int8 | uint8 | int16 | uint16 | int32 | uint32

Grayscale volume, specified as a 3-D numeric array.

Data Types: single | double | int8 | uint8 | int16 | uint16 | int32 | uint32

Reference grayscale intensity value, specified as a scalar.

Data Types: double

Reference grayscale intensity mask, specified as a logical array of the same size as I.

Data Types: logical

Column index of reference pixel (or voxel), specified as a numeric (integer-valued) vector.

Data Types: double

Row index of reference pixel (or voxel), specified as a numeric (integer-valued) vector.

Data Types: double

Plane index of reference voxel, specified as a numeric (integer-valued) vector.

Data Types: double

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: W = graydiffweight(I, seedpointC, seedpointR,'GrayDifferenceCutoff',25);

Output weight roll-off factor, specified as the comma-separated pair consisting of 'RolloffFactor' and a positive scalar of class double. Controls how fast the output weight falls as the function of the absolute difference between an intensity value and the reference grayscale intensity. When viewed as a 2-D plot, pixel intensity values can vary gradually at the edges of regions, creating a gentle slope. In your segmented image, you might want the edge to be more well-defined. Using the roll-off factor, you control the slope of the weight value curve at points where intensity values start to change. If you specify a high value, the output weight values fall off sharply around the regions of change intensity. If you specify a low value, the output weight has a more gradual fall-off around the regions of changing intensity. The suggested range for this parameter is [0.5 4].

Data Types: double

Threshold for absolute grayscale intensity difference values, specified as the comma-separated pair consisting of 'GrayDifferenceCutoff' and a nonnegative scalar of class double. When you put a threshold on intensity difference values, you strongly suppress output weight values greater than the cutoff value. graydiffweight assigns these pixels the smallest weight value. When the output weight array W is used for Fast Marching Method based segmentation (as input to imsegfmm), this parameter can be useful in improving the accuracy of the segmentation output. Default value of this parameter is Inf, which means that there is no hard cutoff.

Data Types: double

## Output Arguments

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Weight array, specified as numeric array of the same size as the input image I or volume V. W is of class double, unless the input image or volume is of class single, in which case W is of class single.

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### Image Segmentation

You can use the weights returned by the graydiffweight function for image segmentation using the imsegfmm function. Segmentation using imsegfmm requires seed locations, provided by the reference grayscale intensity mask or the column and row indices of the reference pixels.

• If you calculate weights with the graydiffweight function using a scalar reference grayscale intensity value, refGrayVal, identify seed locations that have an average intensity value equal to refGrayVal. Specify the column and row indices of the seed locations, C and R respectively, along with a threshold level, thresh, for segmentation using imsegfmm.

W = graydiffweight(I,refGrayVal);
BW = imsegfmm(W,C,R,thresh);

• If you calculate weights with the graydiffweight function using a reference grayscale intensity mask, mask, specify the same mask, along with a threshold level, thresh, for segmentation using imsegfmm.

• If you calculate weights with the graydiffweight function using the column and row indices of reference pixels, C and R respectively, specify the same column and row indices, along with a threshold level, thresh, for segmentation using imsegfmm.

W = graydiffweight(I,C,R);
BW = imsegfmm(W,C,R,thresh);

### Volume Segmentation

You can use the weights returned by the graydiffweight function for volume segmentation using the imsegfmm function. Segmentation using imsegfmm requires seed locations, provided by the column, row, and plane indices of the reference voxels.

• If you calculate weights with the graydiffweight function using the column, row, and plane indices of reference voxels, C, R, and P respectively, specify the same column, row, and plane indices, along with a threshold level, thresh, for segmentation using imsegfmm.

W = graydiffweight(V,C,R,P);
BW = imsegfmm(W,C,R,P,thresh);

## Version History

Introduced in R2014b