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