diff --git a/sim.tex b/sim.tex index da0382b..cac7a28 100644 --- a/sim.tex +++ b/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}