binomial_filter (Operator)

Name

binomial_filter — Smooth an image using the binomial filter.

Synopsis

binomial_filter(Image : ImageBinomial : MaskWidth, MaskHeight : )

Description

binomial_filter smooths the image Image using a binomial filter with a mask size of MaskWidth * MaskHeight pixels and returns the smoothed image in ImageBinomial. The binomial filter is a very good approximation of a Gaussian filter that can be implemented extremely efficiently using only integer operations. Hence, binomial_filter is very fast. Let m = MaskHeight and n = MaskWidth. Then, the filter coefficients b_ij are given by binomial coefficients

/ l \      l!
|   | = ---------
\ k /   k! (l-k)!

as follows:

       1     / m-1 \ / n-1 \
b   = ------ |     | |     |
 ij    n+m-2 \  i  / \  j  /
      2

Here, i = 0, ..., m-1 and j = 0, ..., n-1. The binomial filter performs approximately the same smoothing as a Gaussian filter with sigma = sqrt(n-1)/2, where for simplicity it is assumed that m = n. In detail, the relationship between n and sigma is:

 n  |  sigma
-------------
 3  |  0.7523
 5  |  1.0317
 7  |  1.2505
 9  |  1.4365
11  |  1.6010
13  |  1.7502
15  |  1.8876
17  |  2.0157
19  |  2.1361
21  |  2.2501
23  |  2.3586
25  |  2.4623
27  |  2.5618
29  |  2.6576
31  |  2.7500
33  |  2.8395
35  |  2.9262
37  |  3.0104

If different values are chosen for MaskHeight and MaskWidth, the above relation between n and sigma still holds and refers to the amount of smoothing in the row and column directions.

Parameters

Image (input_object)	(multichannel-)image(-array) → object (byte / uint2)
Input image.

ImageBinomial (output_object)	(multichannel-)image(-array) → object (byte / uint2)
Smoothed image.

MaskWidth (input_control)	integer → (integer)
Filter width.
Default value: 5
List of values: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37

MaskHeight (input_control)	integer → (integer)
Filter height.
Default value: 5
List of values: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37

Result

If the parameter values are correct the operator binomial_filter returns the value 2 (H_MSG_TRUE). The behavior in case of empty input (no input images available) is set via the operator set_system('no_object_result',<Result>). If necessary an exception is raised.

Parallelization Information

binomial_filter is reentrant and automatically parallelized (on tuple level, channel level, domain level).

Possible Predecessors

read_image, grab_image

Possible Successors

regiongrowing, threshold, sub_image, dyn_threshold, auto_threshold

Alternatives

gauss_image, smooth_image, derivate_gauss, isotropic_diffusion

See also

mean_image, anisotropic_diffusion, sigma_image, gen_lowpass

Module

Foundation