Volume Filter

Volume Filter includes several options for smoothing or transforming volume data. See also: Hide Dust, vop, mask, segment

There are several ways to start Volume Filter, a tool in the Volume Data category (including from the Volume Viewer Tools menu).

Filter type:

• Gaussian - perform Gaussian filtering
  • Width - one standard deviation in physical units (such as Å) of the 3D isotropic Gaussian function (the command vop gaussian allows using different widths along X,Y,Z)
  • Value type - whether to produce a map with the same value type as the input, 32-bit float, or 64-bit float
• Median 3x3x3 - smooth the data by setting each value to the median of the 27 values in the enclosing 3x3x3 box of grid cells (the command vop median allows using different box sizes)
  • Iterations - how many cycles of value reassignment to perform
• Bin - reduce data size by averaging the values in NxNxN cells of the original data, where N is the Bin size. Different bin sizes along the different axes can be specified by entering three numbers separated by spaces.
• Laplacian - perform Laplacian filtering
• Fourier Transform - apply Fourier transform
• Scale - change data values (not grid point locations) and/or types:
  • Shift - add a constant to each value; can be negative
  • Scale - multiply values by a factor
  • Value type - cast values to a different value type: int (8-, 16-, or 32-bit), uint (8-, 16-, or 32-bit), or float (32- or 64-bit)
  Pressing return (Enter) in the Shift or Scale value field is equivalent to clicking Filter. Shifting and scaling are applied in that order. Shifting and scaling use 32-bit float to avoid truncation problems.
• Flatten - scale data values by factor (1 + a*i + b*j + c*k) where i,j,k are the grid indices and a,b,c are calculated to zero out the first moments of the resulting map (make its mass balance at the center of the grid)

Clicking Options reveals additional settings (clicking the close button on the right hides them again):

• Displayed subregion only - whether to limit the procedure to the current display region (which could be a subregion of the current set)
• Displayed subsampling only - whether to use only the displayed subsample (when step > 1) instead of the full resolution of the current set
• Adjust threshold for constant volume - adjust the contour level on the result to enclose the same volume as the contour surface on the current set
• Immediate update - update the result as soon as a slider parameter (Gaussian width or median iterations) is changed; only applies when the current set is the result of a previous application of the same type of filtering

Gaussian filtering. Convoluting the data with a Gaussian function improves the ratio of signal to noise but reduces resolution. It is fastest for data sizes that are powers of 2, and can be very slow when insufficient memory is available. It produces a a map with 32-bit floating point values and uses negligible additional memory. It may be helpful to limit the input to just a subsample or subregion of the original data. Although it uses a fast Fourier transform calculation method, it does not use map periodicity. Values outside the map boundaries are treated as zero.

Laplacian filtering. The Laplacian operation is a sum of second derivatives. Laplacian filtering is useful for edge detection but amplifies noise, so it may be necessary to perform smoothing such as Gaussian filtering beforehand. Finite differences v(i-1)-2*v(i)+v(i+1) along each axis are used, and voxels at the edge of the box are set to zero.

Fourier transform. Only the magnitudes of the complex Fourier components are included in the new data set; the phases are discarded and the constant component is set to zero. The box containing the Fourier transform (with axes in units of reciprocal space) is centered on the original data and scaled to have the same total volume. Some properties of the original data are evident from the Fourier transform. High-frequency components are near the edges of the box, low-freqency components near the center. Volume data is typically oversampled (voxel size two to three times smaller than the actual data resolution) and this causes the Fourier transform to have nonzero values only in the middle half or third of its bounding box. The missing wedge in electron microscope tomograms can also be seen. Spikes radiating along the principal axes in the Fourier transform are caused by nonperiodicity of the original data.