Add Perception and Psychophysics section

sim.tex

@@ -324,7 +324,88 @@ All three measures can be visualized by the \emph{recall-precision-graph} or the
 \emph{receiver operating characteristics curve} (ROC curve). The latter plots
 the false positive rate on the x-axis against the true positive rate.
 
-\section{Perception and Psychophysics 600 words}
+\section{Perception and Psychophysics}
+
+The human perception happens in the brain where we have approximately $10^{10}$
+neurons and even more synapses ($10^{13}$). Neurons are connected to around 3\%
+of their neighbors and new connections never cease to be built, unlike neurons
+which are only created up to a young age. The perceptual load on our senses is
+at around 1Gb/s. To deal with all these data, most of the data is ignored and
+only later reconstructed in the brain, if they are needed. The olfactory sense
+requires the most amount of cells, whereas the aural sense requires the least.
+One reason for the low amount of cells for hearing is that the pre-processing in
+our ears is very sophisticated and thus less processing is needed during the
+later stages. Vision also requires a lot of cells (on the order of $10^6$).
+Vision is handled in part by rods (for brightness) and cones (for color). The
+relationship of rods to cones is about 20 to 1, although the ratio varies a lot
+from one human to the next.
+
+Psychophysics is the study of physical stimuli ($=\Phi$) and the sensations and
+perceptions they produce ($=\Psi$). The relationship between the two is not a
+linear, but a logarithmic one and it is described by the Weber-Fechner law
+\eqref{eq:wf-law}.
+
+\begin{equation}
+    \label{eq:wf-law}
+    \Psi = c\cdot\log(\Phi) + a
+\end{equation}
+
+The Weber law \eqref{eq:w-law} states that, in order to get a similar response,
+stimuli have to be increasing in intensity over time.
+
+\begin{equation}
+    \label{eq:w-law}
+    \Delta\Phi = f(\Phi)
+\end{equation}
+
+In later years, Stanley Smith Stevens empirically developed the Stevens' power
+law \eqref{eq:s-power-law} whereby our perception is dependent on a factor $c$
+multiplied with the stimulus which is raised to the power of \emph{Stevens'
+exponent} and added to a constant $b$.
+
+\begin{equation}
+    \label{eq:s-power-law}
+    \Psi = c\cdot\Phi^{a} + b
+\end{equation}
+
+The eye detects incoming visual stimuli with the aforementioned rods and cones.
+Cones are further split into three different types to detect color. Blue cones
+fire upon receiving light in the 420nm range, whereas green cones react to 534nm
+and red cones to 564nm. These wavelengths are only indicative of where the
+visual system reacts the strongest. Furthermore, these numbers are averages of a
+large population of humans, but can be different for individuals. Green and red
+are perceptually very close and it is postulated by scientists that the
+perception of red only recently separated from the perception of green in our
+evolution and is therefore still very close. Visual information that enters the
+retina is first processed by the ganglion cells which do edge detection. They
+receive their information from \emph{bipolar cells} which either pass along the
+signal or block it. The ganglion cells process multiple such signals in a
+neighborhood and detect length and angle of edges. After edge detection the
+signal is forwarded to the visual cortex which does object detection via the
+\emph{ventral pathway} and motion detection via the \emph{dorsal pathway}.
+Before the signal is forwarded to either of the pathways, the occipital cortex
+processes edge information, color blobs, texture and contours. The three-color
+stimulus is converted into a hue, saturation and value encoding. After that
+motion and 3D information is processed. The flow of information is one of
+semantic enrichment, starting from edge detection and ending in motion
+detection. In the ventral pathway an object is detected invariant to its type,
+size, position or occlusion. The dorsal pathway for motion detection has to deal
+with multiple degrees of freedom due to the eye moving on its own and the object
+moving as well.
+
+The ear consists of the ear canal, which does some filtering, the eardrum for
+amplification, the ossicles and the cochlea. The cochlea is the most important
+part because it translates air waves first into liquid waves and then to
+electrical signals which are transferred to the brain. It contains a
+\emph{staircase} on which there are hairs of different lengths. Depending on
+their length they react to either high or low frequencies. Their movement within
+the liquid is then transformed into electrical signals through the tip links.
+The thresholds of hearing exist on the lower end due to physical limits when the
+hairs inside the ear receive a too small stimulus and therefore do not move
+noticeably. The lower threshold is dependent on the received frequency and is
+lowest at around 4kHz, where we hear best. High energies are needed to hear very
+low frequencies. The threshold on the higher end marks the point at which sounds
+become painful and it seeks to protect us from damaging our hearing.
 
 \section{Spectral Features 600 words}