locallapfilt

Fast local Laplacian filtering of images

Syntax

B = locallapfilt(I,sigma,alpha)

B = locallapfilt(I,sigma,alpha,beta)

B = locallapfilt(___,Name=Value)

Description

B = locallapfilt(I,sigma,alpha) filters the grayscale or RGB image I with an edge-aware, fast local Laplacian filter. sigma characterizes the amplitude of edges in I. alpha controls smoothing of details.

B = locallapfilt(I,sigma,alpha,beta) filters the image using beta to control the dynamic range of A.

B = locallapfilt(___,Name=Value) uses name-value arguments to control advanced aspects of the filter.

Examples

Increase Local Contrast of RGB Image Using Local Laplacian Filtering

Import an RGB image

A = imread('peppers.png');

Set parameters of the filter to increase details smaller than 0.4.

sigma = 0.4;
alpha = 0.5;

Use fast local Laplacian filtering

B = locallapfilt(A, sigma, alpha);

Display the original and filtered images side-by-side.

imshowpair(A, B, 'montage')

Increase Local Contrast, Balancing Speed and Quality

Local Laplacian filtering is a computationally intensive algorithm. To speed up processing, locallapfilt approximates the algorithm by discretizing the intensity range into a number of samples defined by the 'NumIntensityLevels' parameter. This parameter can be used to balance speed and quality.

Import an RGB image and display it.

A = imread('peppers.png');
figure
imshow(A)
title('Original Image')

Use a sigma value to process the details and an alpha value to increase the contrast, effectively enhancing the local contrast of the image.

sigma = 0.2;
alpha = 0.3;

Using fewer samples increases the execution speed, but can produce visible artifacts, especially in areas of flat contrast. Time the function using only 20 intensity levels.

t_speed = timeit(@() locallapfilt(A, sigma, alpha, 'NumIntensityLevels', 20))  

t_speed = 
0.0348

Now, process the image and display it.

B_speed = locallapfilt(A, sigma, alpha, 'NumIntensityLevels', 20);
figure
imshow(B_speed)
title(['Enhanced with 20 intensity levels in ' num2str(t_speed) ' sec'])

A larger number of samples yields better looking results at the expense of more processing time. Time the function using 100 intensity levels.

t_quality = timeit(@() locallapfilt(A, sigma, alpha, 'NumIntensityLevels', 100))

t_quality = 
0.1164

Process the image with 100 intensity levels and display it:

B_quality = locallapfilt(A, sigma, alpha, 'NumIntensityLevels', 100);
figure
imshow(B_quality)
title(['Enhancement with 100 intensity levels in ' num2str(t_quality) ' sec'])

Try varying the number of intensity levels on your own images. Try also flattening the contrast (with alpha > 1). You will see that the optimal number of intensity levels is different for every image and varies with alpha. By default, locallapfilt uses a heuristic to balance speed and quality, but it cannot predict the best value for every image.

Boost Local Color Contrast Using 'ColorMode'

Import a color image, reduce its size, and display it.

A = imread('car2.jpg');
A = imresize(A, 0.25);
figure
imshow(A)
title('Original Image')

Set the parameters of the filter to dramatically increase details smaller than 0.3 (out of a normalized range of 0 to 1).

sigma = 0.3;
alpha = 0.1;

Let's compare the two different modes of color filtering. Process the image by filtering its intensity and by filtering each color channel separately:

B_luminance = locallapfilt(A, sigma, alpha);
B_separate  = locallapfilt(A, sigma, alpha, 'ColorMode', 'separate');

Display the filtered images.

figure
imshow(B_luminance)
title('Enhanced by boosting the local luminance contrast')

figure
imshow(B_separate)
title('Enhanced by boosting the local color contrast')

An equal amount of contrast enhancement has been applied to each image, but colors are more saturated when setting 'ColorMode' to 'separate'.

Perform Edge-Aware Noise Reduction

Import an image. Convert the image to floating point so that we can add artificial noise more easily.

A = imread('pout.tif');
A = im2single(A);

Add Gaussian noise with zero mean and 0.001 variance.

A_noisy = imnoise(A, 'gaussian', 0, 0.001);
psnr_noisy = psnr(A_noisy, A);
fprintf('The peak signal-to-noise ratio of the noisy image is %0.4f\n', psnr_noisy);        

The peak signal-to-noise ratio of the noisy image is 30.0234

Set the amplitude of the details to smooth, then set the amount of smoothing to apply.

sigma = 0.1;
alpha = 4.0;

Apply the edge-aware filter.

B = locallapfilt(A_noisy, sigma, alpha);
psnr_denoised = psnr(B, A);
fprintf('The peak signal-to-noise ratio of the denoised image is %0.4f\n', psnr_denoised);

The peak signal-to-noise ratio of the denoised image is 32.3362

Note an improvement in the PSNR of the image.

Display all three images side by side. Observe that details are smoothed and sharp intensity variations along edges are unchanged.

figure
subplot(1,3,1), imshow(A), title('Original')
subplot(1,3,2), imshow(A_noisy), title('Noisy')
subplot(1,3,3), imshow(B), title('Denoised')

Smooth Image Details Without Affecting Edge Sharpness

Import the image, resize it and display it

A = imread('car1.jpg');
A = imresize(A, 0.25);
figure
imshow(A)
title('Original Image')

The car is dirty and covered in markings. Let's try to erase the dust and markings on the body. Set the amplitude of the details to smooth, and set a large amount of smoothing to apply.

sigma = 0.2;
alpha = 5.0;

When smoothing (alpha > 1), the filter produces high quality results with a small number of intensity levels. Set a small number of intensity levels to process the image faster.

numLevels = 16;

Apply the filter.

B = locallapfilt(A, sigma, alpha, 'NumIntensityLevels', numLevels);

Display the "clean" car.

figure
imshow(B)
title('After smoothing details')

Input Arguments

I — Image to filter

2-D grayscale image | 2-D RGB image

Image to filter, specified as a 2-D grayscale image or 2-D RGB image.

Data Types: single | int8 | int16 | uint8 | uint16

sigma — Amplitude of edges

non-negative number

Amplitude of edges, specified as a non-negative number. sigma should be in the range [0, 1] for integer images and for single images defined over the range [0, 1]. For single images defined over a different range [a, b], sigma should also be in the range [a, b].

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

alpha — Smoothing of details

positive number

Smoothing of details, specified as a positive number. Typical values of alpha are in the range [0.01, 10].

Value	Description
alpha less than 1	Increases the details of the input image, effectively enhancing the local contrast of the image without affecting edges or introducing halos.
alpha greater than 1	Smooths details in the input image while preserving crisp edges
alpha equal to 1	The details of the input image are left unchanged.

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

beta — Dynamic range

1 (default) | non-negative number

Dynamic range, specified as a non-negative number. Typical values of beta are in the range [0, 5]. beta affects the dynamic range of A.

Value	Description
beta less than 1	Reduces the amplitude of edges in the image, effectively compressing the dynamic range without affecting details.
beta greater than 1	Expands the dynamic range of the image.
beta equal to 1	Dynamic range of the image is left unchanged. This is the default value.

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.

Example: B = locallapfilt(I,sigma,alpha,ColorMode="separate") filters each color channel independently.

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

Example: B = locallapfilt(I,sigma,alpha,"ColorMode","separate") filters each color channel independently.

ColorMode — Method used to filter RGB images

"luminance" (default) | "separate"

Method used to filter RGB images, specified as one of the following values. This argument has no effect on grayscale images.

Value	Description
"luminance"	locallapfilt converts the input RGB image to grayscale before filtering and reintroduces color after filtering, which changes the contrast of the input image without affecting colors.
"separate"	locallapfilt filters each color channel independently.

Data Types: char | string

NumIntensityLevels — Number of intensity samples

"auto" (default) | positive integer

Number of intensity samples in the dynamic range of the input image, specified as "auto" or positive integer. A higher number of samples gives results closer to exact local Laplacian filtering. A lower number increases the execution speed. Typical values are in the range [10, 100]. If set to "auto", locallapfilt chooses the number of intensity levels automatically to balance quality and speed based on other parameters of the filter.

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

Output Arguments

B — Filtered image

numeric array

Filtered image, returned as a numeric array of the same size and data type as the input image, A.

References

[1] Paris, Sylvain, Samuel W. Hasinoff, and Jan Kautz. Local Laplacian filters: edge-aware image processing with a Laplacian pyramid, ACM Trans. Graph. 30.4 (2011): 68.

[2] Aubry, Mathieu, et al. Fast local laplacian filters: Theory and applications. ACM Transactions on Graphics (TOG) 33.5 (2014): 167.

Version History

Introduced in R2016b

R2022b: Improved performance

The locallapfilt function shows improved performance. For example, this code is about 6.8x faster than in the previous release.

function locallapfiltTimingTest
      A = imread("peppers.png"); 
      locallapfilt(A,0.4,0.5);
end

The approximate execution times are:

R2022a: 0.254 s

R2022b: 0.037 s

The code was timed on a Windows^® 10, Intel^® Xeon^® E5-2683 v4 CPU @ 2.10 GHz test system (two processors) using the timeit function:

timeit(@locallapfiltTimingTest)