Mappings that preserve neighbourhood relationships are relevant in bothpractical and biological contexts. It is important to be clear about precisely what preserving neighbourhoods could mean. We give a definition of a “perfectly neighbourhood preserving” map, which we call a topographic homeomorphism, and prove that this has certain desirable properties. When a topographic homeomorphism does n...

Sensory information is represented in the brain in the form of topographic maps, in which neighboring neurons respond to adjacent external stimuli. In the visual system, the superior colliculus receives topographic projections from the retina and primary visual cortex (V1) that are aligned. Alignment may be achieved through the use of a gradient of shared axon guidance molecules, or through a r...

Raster topographic images consist of a set of layers depicted in arbitrary color. There exist strong correspondence between the color of the layer and its semantic meaning. Often there is a need to separate or extract semantic layers from the map. The separation results in severe artifacts in places where semantic layers would overlap (e.g. elevations lines drawn on top of the topographic map)....

The topographic projection of retinal ganglion cell (RGC) axons to mouse superior colliculus (SC) or chick optic tectum (OT) is formed in three phases: RGC axons overshoot their termination zone (TZ); they exhibit interstitial branching along the axon that is topographically biased for the correct location of their future TZ; and branches arborize preferentially at the TZ and the initial exuber...

Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution...

Optical imaging studies of somatosensory cortex (SI) in primates has led to re-evaluation of our understanding of cortical functional organization. This chapter describes findings showing that somatosensory topography, long a foundation of cortical function, may not be as precise in the awake monkey, suggesting a re-evaluation of the relationship between topographic representation and sensory p...

We consider the topographic clustering task and focus on the problem of its evaluation, which enables to perform model selection: topographic clustering algorithms, from the original Self Organizing Map to its extension based on kernel (STMK), can be viewed in the unified framework of constrained clustering. Exploiting this point of view, we discuss existing quality measures and we propose a ne...

In mammals, topographic maps emerge from initially diffuse projections during development. To gain insight into the mechanisms governing the transition from a diffuse projection to a topographic map, we studied topographic specificity of functional connections during development, using the cat corticorubral system as a model. In the adult cat, rubrospinal neurons in the dorsomedial part of the ...

The construction of topographic models for fitting a model to the data set requires selection of appropriate values for its parameters. Since the parameters control the flexibility of the model, the generalization problem is directly related to parameter selection. This paper addresses this problem, using a novel criterion for monitoring topographic maps in which the key observation is that we ...

Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the map that each particular case favors. These differences have important consequences for the practic...