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# normxcorr2

Normalized 2-D cross-correlation

## Syntax

``C = normxcorr2(template,A)``

## Description

example

````C = normxcorr2(template,A)` computes the normalized cross-correlation of the matrices `template` and `A`. The resulting matrix `C` contains the correlation coefficients.You optionally can compute the normalized cross-correlation using a GPU (requires Parallel Computing Toolbox™). For more information, see Image Processing on a GPU.```

## Examples

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Read two images into the workspace, and convert them to grayscale for use with `normxcorr2`. Display the images side-by-side.

```onion = rgb2gray(imread('onion.png')); peppers = rgb2gray(imread('peppers.png')); imshowpair(peppers,onion,'montage')```

Perform cross-correlation, and display the result as a surface.

```c = normxcorr2(onion,peppers); figure, surf(c), shading flat```

Find the peak in cross-correlation.

`[ypeak, xpeak] = find(c==max(c(:)));`

Account for the padding that `normxcorr2` adds.

```yoffSet = ypeak-size(onion,1); xoffSet = xpeak-size(onion,2);```

Display the matched area.

```figure imshow(peppers); imrect(gca, [xoffSet+1, yoffSet+1, size(onion,2), size(onion,1)]);```

Read two images into `gpuArray`s.

```onion = gpuArray(imread('onion.png')); peppers = gpuArray(imread('peppers.png')); ```

Convert the color images to 2-D grayscale. The `rgb2gray` function accepts `gpuArray`s.

```onion = rgb2gray(onion); peppers = rgb2gray(peppers); ```

Perform cross-correlation, and display the result as a surface.

```c = normxcorr2(onion,peppers); figure, surf(c), shading flat```

Find the peak in cross-correlation.

`[ypeak, xpeak] = find(c==max(c(:)));`

Account for the padding that `normxcorr2` adds.

```yoffSet = ypeak-size(onion,1); xoffSet = xpeak-size(onion,2);```

Move the data back to the CPU for display.

```yoffSet = gather(ypeak-size(onion,1)); xoffSet = gather(xpeak-size(onion,2)); ```

Display the matched area.

```figure imshow(peppers); imrect(gca, [xoffSet+1, yoffSet+1, size(onion,2), size(onion,1)]); ```

## Input Arguments

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Input template, specified as a numeric matrix. The values of `template` cannot all be the same.

To perform the computation using a GPU, specify `template` as a `gpuArray` that contains a numeric matrix.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical`

Input image, specified as a numeric image. `A` must be larger than the matrix `template` for the normalization to be meaningful.

Normalized cross-correlation is an undefined operation in regions where `A` has zero variance over the full extent of the template. In these regions, `normxcorr2` assigns correlation coefficients of zero to the output `C`.

To perform the computation using a GPU, specify `A` as a `gpuArray` that contains a numeric matrix.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical`

## Output Arguments

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Correlation coefficients, returned as a numeric matrix with values in the range [-1, 1].

If the correlation coefficients are computed using a GPU, then `C` is returned as a `gpuArray` containing a numeric matrix with values in the range [-1, 1].

Data Types: `double`

## Algorithms

`normxcorr2` uses the following general procedure [1], [2]:

1. Calculate cross-correlation in the spatial or the frequency domain, depending on size of images.

2. Calculate local sums by precomputing running sums [1].

3. Use local sums to normalize the cross-correlation to get correlation coefficients.

The implementation closely follows the formula from [1]:

`$\gamma \left(u,v\right)=\frac{{\sum }_{x,y}\left[f\left(x,y\right)-{\overline{f}}_{u,v}\right]\left[t\left(x-u,y-v\right)-\overline{t}\right]}{{\left\{{{\sum }_{x,y}\left[f\left(x,y\right)-{\overline{f}}_{u,v}\right]}^{2}{\sum }_{x,y}{\left[t\left(x-u,y-v\right)-\overline{t}\right]}^{2}\right\}}^{0.5}}$`

where

• $f$ is the image.

• $\overline{t}$ is the mean of the template

• ${\overline{f}}_{u,v}$ is the mean of $f\left(x,y\right)$ in the region under the template.

## References

[2] Haralick, Robert M., and Linda G. Shapiro, Computer and Robot Vision, Volume II, Addison-Wesley, 1992, pp. 316-317.