integralBoxFilter

2-D box filtering of integral images

Syntax

B = integralBoxFilter(A)

B = integralBoxFilter(A,filterSize)

B = integralBoxFilter(___,Name,Value)

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(___,Name,Value) uses name-value pairs to control various aspects of the filtering.

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

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: B = integralBoxFilter(A,5,'NormalizationFactor',1);

NormalizationFactor — Normalization factor applied to box filter

1/filterSize.^2, if scalar, and 1/prod(filterSize), if vector (default) | numeric scalar

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

The default 'NormalizationFactor' 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 'NormalizationFactor' to 1. To avoid overflow in such circumstances, consider using double precision images by converting the input image to class 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 'NormalizationFactor' parameter must be a compile-time constant.

GPU Code Generation

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

Usage notes and limitations:

• The 'NormalizationFactor' parameter must be a compile-time constant.

Version History

Introduced in R2015b