Name: WlzDomainMatchMatrix - calculate match values between to domain sets according to type.

Synopsis

WlzDomainMatchMatrix -d <delta> -t <type> -m <matrix-file> -s <scale>-h -v <rows> <cols>

Options

-d	delta value (default 0.01), must be < 1
-m <file>	input the name of a file containing the mixing and contribution matrices - csv format.
-s	data scale factor, useful for heatmap views.
-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 two objects per column are 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.
	= 8 - Area(intersection)
	= 9 - as type(3) if size(d1) < size(d2) else 0
-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

See Also

Bugs: None known