integralBoxFilter

2-D box filtering of integral images

Syntax

B = integralBoxFilter(A)

B = integralBoxFilter(A,filterSize)

B = integralBoxFilter(___,"NormalizationFactor",normFactor)

Description

B = integralBoxFilter(A) filters the integral image A with a 3-by-3 box filter. Returns the filtered image, B.

B = integralBoxFilter(A,filterSize) filters the integral image A with a 2-D box filter with size specified by filterSize.

B = integralBoxFilter(___,"NormalizationFactor",normFactor) also specifies the normalization factor applied to the box filter.

Examples

Filter Integral Image

Read image into the workspace.

A = imread('cameraman.tif');

Pad the image by the radius of the filter neighborhood. This example uses an 11-by-11 filter.

filterSize = [11 11];
padSize = (filterSize-1)/2;
Apad = padarray(A, padSize, 'replicate','both');

Compute the integral image of the padded input image.

intA = integralImage(Apad);

Filter the integral image.

B = integralBoxFilter(intA, filterSize);

Display original image and filtered image.

figure
imshow(A)
title('Original Image')

figure
imshow(B,[])
title('Filtered Image')

Filter Image with Horizontal and Vertical Motion Blur

Read image into the workspace.

 A = imread('cameraman.tif');

Pad the image by radius of the filter neighborhood, calculated (11-1)/2.

padSize = [5 5]; 
Apad = padarray(A, padSize, 'replicate', 'both');

Calculate the integral image of the padded input.

intA = integralImage(Apad);

Filter the integral image with a vertical [11 1] filter.

Bvert = integralBoxFilter(intA, [11 1]);

Crop the output to retain input image size and display it.

Bvert = Bvert(:,6:end-5);

Filter the integral image with a horizontal [1 11] filter.

Bhorz = integralBoxFilter(intA, [1 11]);

Crop the output to retain input image size.

Bhorz = Bhorz(6:end-5,:);

Display the original image and the filtered images.

figure,
imshow(A)
title('Original Image')

figure,
imshow(Bvert,[])
title('Filtered with Vertical Filter')

figure,
imshow(Bhorz,[])
title('Filtered with Horizontal Filter')

Input Arguments

A — Integral image to be filtered

numeric array

Integral image to be filtered, specified as a numeric array of any dimension.

The integral image must be upright — integralBoxFilter does not support rotated integral images. The first row and column of the integral image is assumed to be zero-padded, as returned by integralImage.

Data Types: double

filterSize — Size of box filter

3 (default) | positive, odd integer | 2-element vector of positive, odd integers

Size of box filter, specified as a positive, odd integer or 2-element vector of positive, odd integers. If filterSize is scalar, then integralBoxFilter uses a square box filter.

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

normFactor — Normalization factor applied to box filter

numeric scalar

Normalization factor applied to the box filter, specified as a numeric scalar.

By default, the normalization factor has the value 1/filterSize.^2 when filterSize is a scalar, and 1/prod(filterSize) when filterSize is a vector. The default has the effect of a mean filter — the pixels in the output image are the local means of the image.

To get local area sums, set normFactor to 1. To avoid overflow in such circumstances, consider using double precision images by converting the input image to data type double.

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

Output Arguments

B — Filtered image

numeric array

Filtered image, returned as a numeric array. integralBoxFilter returns only the parts of the filtering that are computed without padding.

Data Types: double

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• integralBoxFilter supports the generation of C code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

• The normFactor argument must be a compile-time constant.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The normFactor argument must be a compile-time constant.

Version History

Introduced in R2015b