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.TH "holder2d" 2 " 17 June 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
holder2d - holder exponents of a measures defined on 2D real signal
.sp
Author: Pascal Mignot - Bertrand Guiheneuf
.sp
This routine computes \fIholder exponents\fP of a measures defined on 2D real signal. Several measures and capacities are available.
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.SH Usage
\f(CR[\fPholder\f(CR]\fP=holder2d(Input,\f(CR[\fPMeas\f(CR]\fP,\f(CR[\fPRes\f(CR]\fP,\f(CR[\fPRef\f(CR]\fP,\f(CR[\fPRefMeas\f(CR]\fP)
.SH Input parameters
.RS
.TP
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\fBInput\fP : real matrix \f(CR[\fPm,n\f(CR]\fP
Contains the signal to be analysed.
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\fBMeas\fP : string
Analysing measure. Must choosen be in
{"sum", "var", "ecart", "min", "max", "iso", "riso",
"asym", "aplat", "contrast", "lognorm", "varlog", "rho",
"pow", "logpow", "frontmax", "frontmin", "diffh", "diffv",
"diffmin", "diffmax"}
(default : "sum")
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\fBres\fP :
Number of resolutions used for the computation. (default : 1)
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\fBRef\fP : real matrix \f(CR[\fPm,n\f(CR]\fP
Contains the reference signal i.e. the signal on which the reference measure
will be computed.
Input and Ref must have the same dimensions.
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\fBRefMeas\fP : string
Reference measure. (default : "sum")
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.SH Output parameters
.RS
.TP
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\fBholder\fP : real matrix \f(CR[\fPm,n\f(CR]\fP
Contains the Holder exponents.
.RE
.SH Description
.SH Introduction
This routines computes holder exponents by regressing an analysing measure (in a log-log plot) at different scales.
Given a pixel, one defines a (square) window around it. The window size is called the resolution.
The specified measure (or capacity) is then evaluated on the set defined by the window.
For example, in the case of the "sum" measure, at resolution 2, a 5x5 square center on a pixel p0 is
extracted from the input image. The mean of the gray levels of the obtained pixels defines the measure
at pixel p0 and resolution 2.
The measure type is thus given by the input parameter \fIMeas\fP whereas the actual measure is obtained through the
input signal.
In the case of a simple measure analysis, the regression is computed with respect to the size of the window, this
corresponds to comparing the analysing measure to the Lebesgue measure.
Nevertheless, it is possible to compute the regression by comparison with a reference measure given by the
last two parameters.
.SH See Also
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