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# imlincomb

Linear combination of images

## Syntax

Z = imlincomb(K1,A1,K2,A2,...,Kn,An)
Z = imlincomb(K1,A1,K2,A2,...,Kn,An,K)
Z = imlincomb(___,output_class)
gpuarrayZ = imlincomb(gpuarrayK,gpuarrayA,___,output_class)

## Description

Z = imlincomb(K1,A1,K2,A2,...,Kn,An) computes

K1*A1 + K2*A2 + ... + Kn*An

where K1, K2, through Kn are real, double scalars and A1, A2, through An are real, nonsparse, numeric arrays with the same class and size. Z has the same class and size as A1 unless A1 is logical, in which case Z is double.

Z = imlincomb(K1,A1,K2,A2,...,Kn,An,K) computes

K1*A1 + K2*A2 + ... + Kn*An + K

where imlincomb adds K, a real, double scalar, to the sum of the products of K1 through Kn and A1 through An.

Z = imlincomb(___,output_class) lets you specify the class of Z. output_class is a string containing the name of a numeric class.

gpuarrayZ = imlincomb(gpuarrayK,gpuarrayA,___,output_class) performs the operation on a GPU, where the input values,gpuarrayK and gpuarrayA, are gpuArrays and the output value, gpuarrayZ is a gpuArray. This syntax requires the Parallel Computing Toolbox™

When performing a series of arithmetic operations on a pair of images, you can achieve more accurate results if you use imlincomb to combine the operations, rather than nesting calls to the individual arithmetic functions, such as imadd. When you nest calls to the arithmetic functions, and the input arrays are of an integer class, each function truncates and rounds the result before passing it to the next function, thus losing accuracy in the final result. imlincomb computes each element of the output Z individually, in double-precision floating point. If Z is an integer array, imlincomb truncates elements of Z that exceed the range of the integer type and rounds off fractional values.

## Examples

### Example 1

Scale an image by a factor of 2.

J = imlincomb(2,I);
imshow(J)

### Example 1 on a GPU

Scale an image by a factor of 2, performing the operation on a GPU.

J = imlincomb(2,I);
imshow(J)

### Example 2

Form a difference image with the zero value shifted to 128.

J = uint8(filter2(fspecial('gaussian'), I));
K = imlincomb(1,I,-1,J,128); % K(r,c) = I(r,c) - J(r,c) + 128
figure, imshow(K)

### Example 2 on a GPU

Form a difference image with the zero value shifted to 128, performing the operation on a GPU.

J = uint8(filter2(fspecial('gaussian'), I));
K = imlincomb(1,I,-1,J,128); % K(r,c) = I(r,c) - J(r,c) + 128
figure, imshow(K)

### Example 3

Add two images with a specified output class.

K = imlincomb(1,I,1,J,'uint16');
figure, imshow(K,[])

### Example 3 on a GPU

Add two images with a specified output class.

K = imlincomb(1,I,1,J,'uint16');
figure, imshow(K,[])

### Example 4

To illustrate how imlincomb performs all the arithmetic operations before truncating the result, compare the results of calculating the average of two arrays, X and Y, using nested arithmetic functions and then using imlincomb.

In the version that uses nested arithmetic functions, imadd adds 255 and 50 and truncates the result to 255 before passing it to imdivide. The average returned in Z(1,1) is 128.

X = uint8([ 255 10 75; 44 225 100]);
Y = uint8([ 50 20 50; 50 50 50 ]);
Z =
128    15    63
47   128    75

imlincomb performs the addition and division in double precision and only truncates the final result. The average returned in Z2(1,1) is 153.

Z2 = imlincomb(.5,X,.5,Y)
Z2 =
153    15    63
47   138    75