anamech to 13

S2/Neuro/VL/NeuroVL5.typ

@@ -38,3 +38,5 @@ In the brain every cell is oriented to a specific point in space.
 
 Next time we will make applications of convolutions and correlations.
 
+Understand Gabor filters
+

S2/Neuro/VL/NeuroVL6.typ

@@ -0,0 +1,77 @@
+// Main VL template
+#import "../preamble.typ": *
+
+// Fix theorems to be shown the right way in this document
+#import "@preview/ctheorems:1.1.3": *
+#show: thmrules
+
+// Main settings call
+#show: conf.with(
+	// May add more flags here in the future
+	num: 6,
+	type: 0, // 0 normal, 1 exercise
+	date: datetime.today().display(),
+	//date: datetime(
+	//	year: 2025,
+	//	month: 5,
+	//	day: 1,
+	//).display(),
+)
+
+= Uebersicht
+
+E: 26.05.2025
+
+The most important operations are convolution
+$
+	h (x) =  integral_(-oo) ^(oo)  f (u) g (x -u) d u =  f (x) compose g (x) =  g (x) compose f (x),\
+	h (x) =  integral_(-oo) ^(oo)  f (u) g (u - x) d u =  g (x) * f (x).
+$
+
+Auto correlation in contrast to the cross correlation
+$
+	h (x) =  integral_(-oo) ^(oo)  f (u) f (u - x) d u.
+$
+
+The Problem for Stereoskpic ist that eyes and cameras project the 3D World onto a 2D surface.
+
+The Procedure is the search algorithm of cross correlation.
+
+This is slow and non neuronal
+
+We left out the epipolar gemoetry here because the eyes are turning when focussing something nearby.
+
+Understand epipolar geometry in the eye and the resulting cross correlation.
+
+= The algorithm for binocular disparity
+
+We take different gabor function which can be expressed in complex numbers
+$
+	G_(l r) (x) =  (1) / (sqrt(2 pi)sigma)  exp((- (x - x_0 )^2 ) / (2 sigma^2 ) ) e ^(i (k x - phi).
+$
+Calculate the convolution
+$
+	M_(l r) (x) =  G_(l r) (x) * f (x).
+$
+The results from the convolution can be added together and be substracted. This is a bit disorted. Then they are run through
+the square function.
+
+Then we get for the 4 cells
+$
+	S_(1) (x) =  "Real parts added together" \
+	S_(3) (x) =  "Imaginary parts added together".
+$
+
+The total result from the cell is
+$
+	C_(l r) (x) =  M_(l) overline(M_(r)).
+$
+Then the disparity gets calculated as
+$
+	D = (C_(l r) ) / (sqrt(C_(l) C_(r) )) =  (M_(l) overline(M_(r) )) / (sqrt(M_(l) overline(M_(l)) M_(r) overline(M_(r) ) )) prop exp(i (phi_(l) - phi_(r) )) 
+$
+
+#note[
+	To check correlation intuitively.\ To correlate two signals mean to shift one signal back and forth relatively to the other and
+	see how much they are the same.
+]

S2/Neuro/VL/NeuroVL7.typ

@@ -0,0 +1,26 @@
+// Main VL template
+#import "../preamble.typ": *
+
+// Fix theorems to be shown the right way in this document
+#import "@preview/ctheorems:1.1.3": *
+#show: thmrules
+
+// Main settings call
+#show: conf.with(
+	// May add more flags here in the future
+	num: 7,
+	type: 0, // 0 normal, 1 exercise
+	date: datetime.today().display(),
+	//date: datetime(
+	//	year: 2025,
+	//	month: 5,
+	//	day: 1,
+	//).display(),
+)
+
+= Uebersicht
+
+The Perceptron Problem.
+
+The XOR Problem in neuroscience.
+