Super-specific Gabor stuff.
This commit is contained in:
parent
015a3032c1
commit
d56ba575ad
25
main.aux
25
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@ -221,21 +221,22 @@
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Feature extraction by individual neurons}{7}{}\protected@file@percent }
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\newlabel{eq:conv}{{5}{8}{}{}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces \relax }}{8}{}\protected@file@percent }
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\newlabel{eq:toy_log}{{13}{10}{}{}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Threshold nonlinearity \& temporal averaging}{10}{}\protected@file@percent }
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\newlabel{eq:pdf_split}{{15}{11}{}{}{}}
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\newlabel{eq:pdf}{{16}{11}{}{}{}}
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\newlabel{eq:feat_avg}{{17}{11}{}{}{}}
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\newlabel{eq:feat_prop}{{18}{11}{}{}{}}
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\newlabel{eq:toy_env}{{12}{10}{}{}{}}
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\newlabel{eq:toy_snr}{{13}{10}{}{}{}}
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\newlabel{eq:toy_log}{{14}{10}{}{}{}}
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\newlabel{eq:toy_highpass}{{15}{10}{}{}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Threshold nonlinearity \& temporal averaging}{11}{}\protected@file@percent }
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\newlabel{eq:pdf_split}{{16}{11}{}{}{}}
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\newlabel{eq:pdf}{{17}{11}{}{}{}}
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\newlabel{eq:feat_avg}{{18}{11}{}{}{}}
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\newlabel{eq:feat_prop}{{19}{12}{}{}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {4}Discriminating species-specific song\\patterns in feature space}{13}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {5}Conclusions \& outlook}{13}{}\protected@file@percent }
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@ -729,8 +729,46 @@
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\field{pages}{17332\bibrangedash 17344}
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{{un=0,uniquepart=base,hash=376cc9f4803f0227f679089e863cbce8}{%
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givenun=0}}%
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\list{publisher}{1}{%
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{Society for Neuroscience}%
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\field{labeldatesource}{}
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\field{labelnamesource}{author}
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\field{labeltitlesource}{title}
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\field{journaltitle}{Journal of Neuroscience}
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\field{number}{34}
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\field{title}{Input-driven components of spike-frequency adaptation can be unmasked in vivo}
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\field{volume}{24}
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\field{year}{2004}
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\field{pages}{7435\bibrangedash 7444}
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\range{pages}{10}
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\endentry
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\entry{gollisch2002energy}{article}{}
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{{un=0,uniquepart=base,hash=376cc9f4803f0227f679089e863cbce8}{%
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family={Gollisch},
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@ -756,11 +794,11 @@
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[0] Config.pm:307> INFO - This is Biber 2.19
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[0] Config.pm:310> INFO - Logfile is 'main.blg'
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[34] biber:340> INFO - === Mi Feb 11, 2026, 16:04:58
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# Fdb version 4
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"main.bbl"
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"main.blg"
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@ -72,6 +72,8 @@
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\newcommand{\kpi}{\kp_i} % Specific Gabor kernel phase
|
||||
\newcommand{\kni}{\kn_i} % Specific Gabor kernel lobe number
|
||||
\newcommand{\ksi}{\ks_i} % Specific Gabor kernel sign
|
||||
\newcommand{\rh}{\text{RH}} % Relative Gaussian height for FWRH
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\newcommand{\fwrh}{\text{FWRH}} % Gaussian full-width at relative height
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% Math shorthands - Threshold nonlinearity:
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\newcommand{\thr}{\Theta_i} % Step function threshold value
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@ -415,25 +417,38 @@ matching, can be modelled as a convolution
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||||
\label{eq:conv}
|
||||
\end{equation}
|
||||
of the intensity-adapted envelope $\adapt(t)$ with a kernel $k_i(t)$ per
|
||||
ascending neuron. We used Gabor kernels as basis functions for creating
|
||||
different preferred patterns. An arbitrary one-dimensional, real Gabor kernel
|
||||
is generated by multiplication of a Gaussian envelope and a sinusoidal carrier
|
||||
ascending neuron. We use Gabor kernels as basis functions for creating
|
||||
different template patterns. An arbitrary one-dimensional, real Gabor kernel is
|
||||
generated by multiplication of a Gaussian envelope and a sinusoidal carrier
|
||||
\begin{equation}
|
||||
k_i(t,\,\kwi,\,\kfi,\,\kpi)\,=\,e^{-\frac{t^{2}}{2{\kwi}^{2}}}\,\cdot\,\sin(\kfi\,t\,+\,\kpi), \qquad \kfi\,=\,2\pi f_{sin}
|
||||
\label{eq:gabor}
|
||||
\end{equation}
|
||||
with Gaussian standard deviation or kernel width $\kwi$, carrier frequency
|
||||
$\kfi$, and carrier phase $\kpi$. Different combinations of $\kwi$, $\kfi$, and
|
||||
$\kpi$ result in Gabor kernels with different lobe number $\kni$ and sign
|
||||
$\ksi$. If the function space is constrained to only include mirror- or
|
||||
point-symmetric Gabor kernels, frequency $\kf$ is related to lobe number $\kn$
|
||||
by
|
||||
$\kfi$, and carrier phase $\kpi$. Different combinations of $\kw$, $\kf$, and
|
||||
$\kp$ result in Gabor kernels with different lobe number $\kn$, which is the
|
||||
number of half-periods of the carrier that fit under the Gaussian envelope
|
||||
within reasonable limits of attenuation. These limits are a matter of
|
||||
definition, since the Gaussian function never fully decays to zero. A good
|
||||
measure is the Gaussian full-width at relative height, which can be calculated
|
||||
as
|
||||
\begin{equation}
|
||||
\fwrh(\kw,\,\rh)\,=\,2\,\cdot\,\sqrt{-2\,\ln \rh}\cdot\,\kw, \qquad \rh\,\in\,(0,\,1]
|
||||
\end{equation}
|
||||
With this, an appropriate carrier frequency $\kf$ for obtaining a Gabor kernel
|
||||
with width $\kw$ and a desired lobe number $\kn$ can be approximated as
|
||||
\begin{equation}
|
||||
\kf(\kn,\,\fwrh)\,=\,\frac{0.5\,\cdot\,\kn\,+\,0.5}{\fwrh}
|
||||
\end{equation}
|
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We restrict the Gabor kernels to be either even functions~(mirror-symmetric,
|
||||
uneven $\kn$) or odd functions~(point-symmetric, even $\kn$). Under this
|
||||
condition, phase $\kp$ is related to lobe number $\kn$ by
|
||||
\begin{equation}
|
||||
\kp(\kn,\,\ks)\,=\,0.5\,\cdot\,(1\,-\,\text{mod}[\kn,\,2]\,+\,\ks)
|
||||
\label{eq:gabor_phase}
|
||||
\end{equation}
|
||||
which results in the specific phase values shown in
|
||||
Table\,\mbox{\ref{tab:gabor_phases}}.
|
||||
|
||||
Table\,\mbox{\ref{tab:gabor_phase}}.
|
||||
\FloatBarrier
|
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\begin{table}[!ht]
|
||||
\centering
|
||||
@ -447,14 +462,10 @@ Table\,\mbox{\ref{tab:gabor_phases}}.
|
||||
-1 & $-\pi\,/\,2$ & $0$\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\label{tab:gabor_phases}
|
||||
\label{tab:gabor_phase}
|
||||
\end{table}
|
||||
\FloatBarrier
|
||||
In order to create a Gabor kernel with a specific lobe number $\kn$ and kernel
|
||||
width $\kw$, frequency $\kf$ has to be set to
|
||||
\begin{equation}
|
||||
\kf(\kn,\,\kw)\,=\,\frac{\kn}{2\pi\,\kw}
|
||||
\end{equation}
|
||||
|
||||
|
||||
\textbf{Stage-specific processing steps and functional approximations:}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user