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+# $Id$
+function [V, H] = deriche(img, alpha)
+# OUTPUT 
+#  V -> vertical gradient
+#  H -> horizontal gradient
+# 
+# INPUT
+#  img    -> input image (as matrix of doubles) 
+#  alpha  -> filter paramter (scale)
+#
+# Deriche 2D image gradient using recursive filters. Precessing time is 
+# independent of alpha.
+# taken from:
+# Klette, Zamperoni: Handbuch der Operatoren für die Bildverarbeitung, vieweg 
+# 2.Aufl. 1995 pp 224-229
+# algorithm: Deriche R.: Fast algorithms for low-level vision: IEEE Trans. 
+# PAMI-12 (1990) pp 78-87
+#
+# Due to the inherent recursive nature of the algorithms the octave 
+# implementation is rather slow compared to a C implementation although I have
+# vectorized it as far as possible at the expense of memory consuption. As a 
+# side effect the evaluation order had to be modified compared to the Klette / 
+# Zamperoni approach. (A C Implementation can easily process PAL a video stream in 
+# realtime on moderate hardware.)
+#
+# (C)opyright Christian Kotz 2006
+# This code has no warrany whatsoever.
+# Do what you like with this code as long as you
+# leave this copyright in place.
+#
+# author:   Christian Kotz
+# date:     11/21/2006
+# version:  0.1
+#
+## $Log$
+## Revision 1.1  2006/12/03 10:53:14  cocus
+## initial m-file implementetaion.
+##
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; if not, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+if nargin < 2
+  alpha = 1.0
+end
+
+   a   =  -(1-exp(-alpha))^2;
+   b1 =  -2*exp(-alpha);
+   b2 = exp(-2*alpha);
+   a0 = -alpha / (1 - alpha * b1 - b2);
+   a1 = a0 * (alpha-1)*exp(-alpha);
+   a2 = a1 - a0 * b1;
+   a3 = -a0 * b2;
+   
+
+  [n m] = size(img);
+  
+  g_v1 = zeros(n,m);
+  g_v2 = zeros(n,m);
+  g_h1 = zeros(n,m);
+  g_h2 = zeros(n,m);
+  g_hv = zeros(n,m);
+  H = zeros(n,m);
+  V = zeros(n,m);  
+  
+  for k=3:m
+    g_v1(:,k) = img(:, k-1) - b1 * g_v1(:,k-1)- b2 * g_v1(:,k-2);
+  end;
+
+  for k=m-2:-1:1
+    g_v2(:,k) = img(:, k+1) - b1 * g_v2(:,k+1)- b2 * g_v2(:,k+2);
+  end;
+  
+  g_hv = a * (g_v1 - g_v2);
+
+   for k=3:n
+     g_h1(k,:) = a0 * g_hv(k,:) + a1 * g_hv(k-1,:) - b1 *  g_h1(k-1,:) - b2 * g_h1(k-2,:);
+  end;
+  for k=n-2:-1:1
+     g_h1(k,:) = a2 * g_hv(k+1,:) + a3 * g_hv(k+2,:) - b1 *  g_h2(k+1,:) - b2 * g_h2(k+2,:);
+  end;
+
+H = g_h1 + g_h2;
+  
+  for k=3:n
+    g_v1(k,:) = img(k-1,:) - b1 * g_v1(k-1,:)- b2 * g_v1(k-2,:);
+  end;
+
+  for k=n-2:-1:1
+    g_v2(k,:) = img(k+1,:) - b1 * g_v2(k+1,:)- b2 * g_v2(k+2,:);
+  end;
+  
+  g_hv = a * (g_v1 - g_v2);
+
+   for k=3:m
+     g_h1(:,k) = a0 * g_hv(:,k) + a1 * g_hv(:,k-1) - b1 *  g_h1(:,k-1) - b2 * g_h1(:,k-2);
+  end;
+  for k=m-2:-1:1
+     g_h1(:,k) = a2 * g_hv(:,k+1) + a3 * g_hv(:,k+2) - b1 *  g_h2(:,k+1) - b2 * g_h2(:,k+2);
+  end;
+
+V = g_h1 + g_h2;
+
+
+
+
+