A1-ArielRokem
From CS294-10 Visualization Fa07
I have chosen two images from my field of study - the neurobiology of the visual system. Both of the images try to deal with the fact that the system contains multiple representations of the visual field in what seems like a hierarchical organization. They both try to deal with huge amounts of data and with the collapse of a three dimensional structure (the brain) onto a two-dimensional surface of the page.
[edit] Suboptimal Visualization
The Following image is a classic of vision science. It is taken from a landmark paper by Felleman and Van Essen in 1991. It is a circuit diagram of the visual system:
This image is often used in talks in vision science and neuroscience in order to say something like "look how complicated it is. How does anyone expect to ever understand all this?".
The data represented in the image is collected from many different papers, detailing the anatomical connectivity between different areas. Each box in the image represents an area of the brain. Lines in the circuit diagram represent connections. The different levels in height are supposed to represent levels of the hierarchy, but beyond the first few levels of the hierarchy it is hard to say what the reasoning is in dividing up the hierarchy. Ultimately, the only information that is readily available to the viewer is that the system is very intricate. It does not tell us a lot about the spatial relations between the areas. The circuit diagram is just way too intricate to actually supply any information about the connectivity. The use of color in the diagram is rather poor - the red connections signify inhibitory connections, while the black connections are excitatory. The colors of the boxes are somewhat arbitrary, although the spatial location on the diagram (left vs. right) gives some indication of segregation of information in the system.
Deconstruction and Critique
The data described in this image is a set of names of 46 anatomical structures belonging to the visual system (Nominal) and the connectivity matrix between them (which is a 2-d variable - is there a connection between area x and area y, or not and if there is a connection is it excitatory or inhibitory). Additionally, for each area there are the x,y,z coordinates of the area within the brain (all of them quantitative). The data set has 46 (area names) + 46*46= 2116 (connectivity matrix) + 46*3 (x,y,z coordinates) = 2300 data entries. The image model is such that the connectivity is coded by lines connecting the nodes, the x,y,z coordinates in the brain are only very roughly coded by location in the image. Instead, the most salient information coded by spatial location in the image is the number of connections between an area and the eye. The spatial location in the brain is very roughly encoded by the horizontal location of the nodes, where nodes on far horizontal ends of the image tend to be far away on the image. Color of the nodes does not code any information.
Redesign
In my redesign, I have decided to remove the color information that existed in the original image. Then, I added a nominal variable of the rough location of the anatomical structure in the brain (the lobe or sub-cortical structure to which each node in the diagram belongs) and encoded that variable by shading the background behind all the nodes belonging to the same anatomical structure. I have maintained the tangled web of connections that existed in the original image, maintaining the information in the connectivity matrix. Finally, I have added another nominal variable, which is the functional subdivision to which the nodes belong. This is encoded by an addition of two arrows in the image, which denote the two major functional subdivisions of the visual system and roughly denotes which structures belong to which functional subdivision. The vagueness in the location and the direction of the arrows also reflects the lack of agreement on each and every detail of this functional subdivision
[edit] Near-optimal Visualization
The other image is taken from a recent paper from Larsson and Heeger. They use a computational method in order to unfold the surface of the brain and show a flattened representation of the few first areas in the Felleman and Van Essen scheme:
These images are maps of the cortical surface of one half of the visual cortex. The topography of the cortex is indicated in shades of gray, in the background. A compass in the center of the image gives us the anatomical coordinates of these maps. The left column is a map of representation in the polar angle domain and the map on the right is the preference in the eccentricity domain. The colours on the maps represent locations in the visual field, represented by that area of the cortical surface. The key, one for the eccentricity and one for the polar angle, is in the two colour wheels at the bottom of the figure. The two top panels are examples of maps from two individuals and the two bottom maps are averaged across 15 subjects. The image preserves the anatomical relations between the different visual areas, showing the point of segregation in the visual system (that is the branching between V3A/B and LO1 at the top of the image. Notice that the two areas LO1 and LO2 were both unknown to science before these maps were created. In fact, this visualization of these areas (probably) puts an end to a long dispute in the scientific literature on the homology between human and monkey brains. The model is then even more clearly visualized in the following gray scale image:
So - while this method of visualization actually illuminates new facts about the world that may be concealed in the data, the Felleman and Van Essen visualization doesn't actually tell us anything that we didn't previously know about the system. Primarily, that it is rather complicated.
Deconstruction
I will refer to the first image in this section. This figure includes staggering amounts of data. The measurements presented here represent hundreds of time points measured from tens of thousands of spatial locations in the brain. The data is measurements of the preferred spatial locations in the visual field among cells in various spatial locations in the cerebral cortex. The 3-d locations in the brain have been flattened to locations on a contiguous 2-d map. In addition to the spatial location in the visual and on the surface of this map, there is also information about the 3-d curvature associated with this area in the 3-d brain. So - the data model is: 2-d location in the visual field. This is divided into two: the eccentricity preference(quantitative, ratio-scale. The point where the person is fixating is zero) and the angular position (quantitative - the zero point is arbitrarily assigned to some angular position). X,Y coordinates on the brain (quantitative) and curvature (quantitative). The image model is based on dividing the map into two maps: one represents the eccentricity map and the other represents the angular position preference. These are represented by a color scale. Though this color scale is arbitrary, there is a legend on the image itself. Curvature is encoded in a gray-scale. The spatial location in the brain is encoded as x,y coordinates on the map. In addition, there is the nominal variable of names of brain areas, encoded as tags with arrow-heads to the area. The borders between areas are in fact ordinal variables, as they correspond to meridia in the visual field. These are encoded by the texture of the lines denoting the borders between areas. The area of the brain representing the center of the visual field is denoted by a circle. In addition there is a weather-dial showing the orientation of all the images on the page with respect to the head and two scale bars, one for size relative to the brain and one with regard to the size of the eccentricity relative to the visual field.
