Woolz Image Processing  Version 1.7.5
Name
WlzDomainMatch - calculate a match values between to domains or domain sets according to type.
Synopsis
WlzDomainMatch -d <delta> -t <type> -m <matrix-file> -s <scale> -h -v
Options
 -d delta value (default 0.01), must be < 1 -m input the name of a file containing the mixing and contribution matrices - csv format. -t type parameter to determine match function (default 1), values: = 1 - Area(intersection)/Area(union) = 2 - if Area(d1) > Area(d2) as type=1 else inverse = 3 - Area(intersection)/Area(d1) = 4 - Area(intersection)/Area(d2) = 5 - Comparative match between two targets given by the ratio of type 4 matchs to each domain. For this option a 3rd object is required in the input stream. = 6 - use the input mixing and contributing matrices. The matrix dimensions must match the number of categories in the category image data. Note the matrices do not need to be square. -h Help - print help message -v Verbose operation
Description
Read in domains or index images from stdin, calculate the match value according to type and write the calculated value to stdout. The match functions are:

$V_1 = \frac{S(d_1 \wedge d_2)}{S(d_1 \vee d_2)}$

$V_2 = \left \{ \begin{array}{r@{\quad if \quad}l} V_1 & S(d_1) \ge S(d_2) \\ \frac{1}{V_1} & S(d_1) < S(d_2) \end{array} \right.$

$V_3 = \frac{S(d_1 \wedge d_2)}{S(d_1)}$

$V_4 = \frac{S(d_1 \wedge d_2)}{S(d_2)}$

$V_5 = \left \{ \begin{array}{c@{\quad : \quad}l} 1.0 & S(d_2) = 0 \quad\mbox{or}\quad S(d_3) = 0, \\ 1 / \delta & S(d_2) = 0 \quad\mbox{and}\quad S(d_1 \wedge d_3) = 0, \\ \delta & S(d_3) = 0 \quad\mbox{and}\quad S(d_1 \wedge d_2) = 0, \\ \frac{S(d_1 \wedge d_2)}{S(d_2)} \times \frac{S(d_3)}{S(d_1 \wedge d_3)} & \mbox{otherwise}. \\ \end{array} \right.$

\begin{eqnarray*} V_6 & = & \frac{\sum_{Pixels} M_{ll'}}{A_{contrib}} \quad\mbox{where}\\ A_{contrib} & = & \sum_{Pixels} \left \{ \begin{array}{c@{\quad \mbox{if} \quad}l} 1 & C_{ll'} \ne 0,\\ 0 & C_{ll'} = 0, \end{array}\right. \end{eqnarray*}

In these formulae the $$S()$$ is the size of the domain - volume or area depending on the nature of the image. $$l, l'$$ are the pixel values of the two input category images.
Examples