Filter 3D

Overview

Filter3D provides a set of three-dimensional filters, operations which for each pixel in the output calculate an intensity based on the input intensities in a box-shaped region about the pixel. The same filters are available as in Filter 2D, including mean and median filters. The size of the region is set by the XY and Z kernel size fields. The three dimensions used for filtering can either be x, y, and z or x, y, and time. You can switch between the two with the toggle button labeled "swap z/time". Filtering over x, y, and z is the default when the input file has more than one z section per time point or only one time point.

Filter 3D's user interface uses the same set of controls for selecting and processing a region as other Priism applications.

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Method

The available filter types are listed below. More details and examples of the results on two-dimensional data are in the Filter 2D documentation.

Median

The median filter looks at the image intensities within a box-shaped region around each pixel and selects the median value for the resulting image. When the enhance toggle is on, the result is the input times a scale factor minus the selected median.

Mean

The mean filter is similar to the median filter except that the mean value is used instead of the median.

Gaussian

When the enhance toggle is off, the Gaussian filter replaces a value with the weighted average of it and the neighboring pixels; the weights fall off exponentially as the square of the distance divided by 2 times the square of sigma. When the enhance toggle is on, the result is the input times a scale factor minus the weighted average.

Laplacian (LoG)

The Laplacian filter implemented here is an approximation to the negative of the Laplacian operator. The Laplacian operator has the useful property that a location where the output values change sign marks the position of an edge. The Laplacian operator involves the computation of differences and therefore tends to amplify noise. If sigma is greater than zero, the Laplacian is combined with a Gaussian smoothing step to give what is known as the Laplacian of Gaussian or LoG filter; this is useful for reducing the amount of noise introduced.

When the Enhance toggle is on, the scale factor times the input minus the result of the of the filter is computed. This is one way to enhance edges in an image; another, likely better, method is to use the EdgeEnh application.

Avg. Deviation

When the enhance toggle is off, the output is an unbiased estimate of the average absolute deviation from the local mean. When the enhance toggle is on, the output is the average absolute deviation from the input intensity at that point.

Weighted Mean

See the Filter 2D documentation for how this filter is defined - the name is probably a misnomer but it is what was used in previous versions of Filter 2D. If you know a use or a rationale for this particular filter, let the Priism maintainers know.

Minimum

When the enhance toggle is off, the minimum filter replaces a value with the minimum value in the neighborhood. If the input is a binary image (values are either one or zero), the minimum filter is equivalent to the morphological erosion operator with a square structuring element. When the enhance toggle is on, the result is the input times a scale factor minus the neighborhood minimum.

Maximum

When the enhance toggle is off, the maximum filter replaces a value with the maximum value in the neighborhood. If the input is a binary image (values are either one or zero), the maximum filter is equivalent to the morphological dilation operator with a square structuring element. When the enhance toggle is on, the result is the input times a scale factor minus the neighborhood maximum.

Bilateral

The bilateral filter implements the filter described in

Tomasi, C. and Manduchi, R. "Bilateral Filtering for Gray and Color Images." Proceedings of the 1998 IEEE International Conference on Computer Vision, Bombay, India. Pages 839 - 846.

The filter replaces the value at a pixel, (i, j, k), with a weighted sum of the pixel values in the neighborhood. Each weight is the product of a factor dependent on the distance (in pixels) to (i, j, k) and another factor dependent on the difference in intensity with the pixel at (i, j, k). This implementation of the bilateral filter uses Gaussian functions for both components of the weight. The values in the "Sigma XY/Z (pix)" field control the standard deviations for the Gaussian weighting as a function of distance, and the value in the "Intensity sigma" field controls the standard deviation for the Gaussian weighting as a function of intensity difference.

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Swap Z/Time

The three dimensions used for filtering can either be x, y, and z or x, y, and time. When the toggle button labeled "swap z/time" is off, the program uses x, y, and z as the dimensions to filter. When that toggle button is on, the program uses x, y, and time as the dimensions to filter. When you select a new input file, the program will automatically select the dimension to use as the third dimension. If the file has more than one z section or only one time point, the program will use the z dimension as the third dimension; otherwise, it will use the time dimension as the third dimension.

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Enhance

When the Enhance toggle is on the result for each iteration is the input data for that iteration times a scale factor minus what the result would be when the toggle was off. The average deviation filter is an exception to this.

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Scale Factor

If the Enhance toggle is on and the filter is not an average deviation filter, the result of an iteration is the input data for that iteration times the scale factor minus the filtered input data.

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Sigma

For the Gaussian and Laplacian (LoG), and bilateral filters the width is controlled by the value of sigma in a given dimension. Larger values of sigma give broader filters. The values of sigma for the x and y directions are the same; in the z (or time) direction the value of sigma can be given a different value.

When the autosize toggle is on, any changes to the sigma values will automatically calculate a kernel size to give a reasonable approximation for the filter.

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Intensity Sigma

The value in the "Intensity sigma" field only affects the bilateral filter. The bilateral filter tends to reduce the magnitude of intensity changes that are less than the intensity sigma and preserve the magnitude of intensity changes that are much greater than the intensity sigma.

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Kernel Size

The kernel size is the size, in pixels, of the box used to calculate the filtered images. The box has a square cross section in x and y; the square has a side length given by the value in the XY kernel size field. The height of the box (i.e. the width of the filter in the z or time dimension) is given by the value in the Z kernel size field.

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Iterations

The filter is applied repeatedly with the output from the previous pass becoming the input for the next. The number of passes is shown in the Iterations field.

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Command Line

Filter 3D accepts the command-line arguments described in Region.html. In addition, Filter 3D has the following options (optional parts are shown in brackets):

-3d=z or -3d=t

Selects which dimension to use as the third dimension for processing. The first form selects the z dimension as the third dimension; the second form selects the time dimension as the third dimension. If you do not specify either form, the program uses the z dimension as the third dimension when the input file has multiple z sections per time point or only one time point. Otherwise, the program uses the time dimension as the third dimension for filtering.

-enhance

If specified, the result of each iteration of filtering is the input data for that iteration minus what the result would be without -enhance specified. The average deviation filter is an exception to this.

-iterations=n

Specifies that the filtering should be performed for n iterations. If the command line does not contain -iterations, one iteration of filtering is performed.

-kernel_size=nx[:ny:nz]

Sets the size of the kernel to be nx by ny by nz (or, if ny and nz are not specified, nx by nx by nx). If -kernel_size is not supplied on the command-line, the kernel size will be determined from the sigma values (see below) for the Gaussian, Laplacian (LoG), and bilateral filters and will be 3x3x3 for all other filter types.

-method=filter_type

Sets what form of filtering to apply. Possible values for filter_type are:

median: Use a median filter.
mean: Use a mean filter.
gaussian: Use a Gaussian filter.
laplacian: Use a Laplacian (LoG) filter.
avgdev: Use an average deviation filter.
wghtmean: Use a weighted mean filter.
minimum: Use a minimum filter.
maximum: Use a maximum filter.
bilateral: Use a bilateral filter.

-scale=value

Sets the scale factor used when -enhance is used and the filter is not an average deviation filter. If not supplied, the scale factor defaults to one.

-sigma=sigma_x[:sigma_y:sigma_z]

Sets how rapidly the Gaussian, Laplacian (LoG), and bilateral filters fall off to zero. If sigma_y and sigma_z are not supplied, they are set to the value of sigma_x. If -sigma is not specified on the command-line, the default value of sigma in all three directions is one.

-sigma_inten=s

Sets the intensity sigma, the standard deviation of the Gaussian for the intensity weighting component of the bilateral filter. s must be a number greater than or equal to zero. If you do not specify the -sigma_inten option on the command line, Filter3D uses a value of five for the intensity sigma.

As an example, the following command-line applies two iterations of a 5x5x3 mean filter to raw.dat and places the results in image window 1:

    Filter3D raw.dat 1 -method=mean -kernel_size=5:5:3

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