``two-vol. comparison'' -- find differences between two volumes

purpose:

Computes the various types of comparisons between two volumes. These comparisons are:

1. Average error. Compute the average gray-level difference between voxels in two volumes; i.e. compute the average value of the quantity , where v1 and v2 are the input volumes and represents the voxel location.
2. Number of close voxels. Calculate the number of voxels in both volumes whose intensity difference is within a set threshold; i.e. tabulate the number of voxels that satisfy the constraint intensity spread.
3. Total-volume difference. Calculate the number of voxels that have a gray-level > 0 in one volume and gray-level equal to zero in the other. This corresponds to the volume difference measure D1 in the Higgins proposal [9], defined as where and are segmented regions in the two volumes. Note that, for this function, any non-zero voxel in a volume is considered a part of the segmented region of that volume.
4. Half-volume difference. Calculate the number of voxels that satisfy and , where v1 and v2 are the first and second input volumes, respectively. This corresponds to the volume-difference measure in the Higgins proposal [9], defined as where and are defined as in (3), above.
5. 3-D distance-weighted volume difference (DWVD). Find the voxels that satisfy the total-volume difference constraint , and calculate their volume, weighing each non-mutual voxel by its 26-connected distance from the border of the first volume. This corresponds to the volume-difference measure in the Higgins proposal [9], defined as

   

   where

   

   and is defined as the shortest distance from the point to a point on , the boundary of .

   -D distance-weighted volume difference. Similar to the 3-D DWVD, above, except it performs the calculations on 2-D slices of a 3-D image.

For functions 3-6 the error volume can be output as an absolute error volume or as a ratio of the first volume.

input:

Depends on the particular function:
For functions 1 and 2: Two 8-bit grayscale volumes.
For functions 3-6: Two 8-bit binary (segmented) volumes.

output:

A text file containing the requested information. The available functions output the following files, where XXXXXX is a random sequence of characters:

Average error (function 1): aveXXXXXX
* Close voxels (function 2): closeXXXXXX
* Volume differences (functions 3-6): diffXXXXXX
*

The DWVD functions (5-6) will also produce an output image. This image has gray-level intensities representing the distance from the border of the first volume to points outside of the volume, with points interior to the border being set to 1. For example, if a voxel in the output image has a gray-level intensity of 5, then it is 5 voxels away from the nearest border voxel of the first volume.

distance algorithms:

A fast algorithm originally proposed by Vincent [30] was used to compute the required 8--connected distances for the 2--D distance--weighted volume difference calculations. This algorithm was modified to work with 3--D 26-connected distances to expedite computation of the 3--D distance--weighted volume difference measurements. Refer to [30] and the source code (see comments) for more information on these functions.

parameters:

The default parameters menu is

first volume = 0
* second volume = 0
* function = average error
*
* * Parameters for [2] # close voxels *
* intensity spread = 0
*
* * Parameters for [3-6] volume differences *
* result calculated as = ratio of volume #1
*
* * Parameters for [5-6] DWVD functions *
* maximum distance to consider = 255
*

The parameter ``function = '' toggles between the available functions define above.
The ``intensity spread ='' parameter is applicable only for the close voxels function, and defines the theshold of gray-level difference between the two volumes.
``result calculated as ='' defines the volume difference output as a ratio of the first volume or as an absolute error volume.
The final parameter ``maximum distance to consider ='' specifies the maximum distance a voxel can be weighted by in the distance-weighted volume difference calculations.

comments:

 

1. All functions available here, except for the 3-D distance-weighted volume difference, are very fast.
2. The 3-D distance-weighted volume difference will take less than one minute for images of a million voxels or less.
3. The 2--D DWVD function (6) utilizes a fast distance calculating algorithm proposed by Vincent [30] to compute the desired distance map. A source--code module named dist_2d.c computes this distance map, which is available along with other source-code modules for the ROI other category.
4. The 3--D DWVD function available in (5) computes distances through a modification to the Vincent algorithm. The source--code module dist_3d.c performs the 3--D distance calculations in either 6-- or 26--connectivity, and is also available in the other category of ROI.
5. Finally, another distance map calculator for 3--D is available. This function,
   [4] dist_3d_morph.c, uses a successive erosionaddition algorithm to compute the 26--connected distance map for a volume. This was the original method for computing distance maps within ROI before it was replaced by the fast algorithm. This function is also available in the ROI other category.
6. These distance mapping algorithms used by the distance-weighted volume difference functions are general and can be utilized by other routines if desired. They are available in the ROI libraries.