Sensor fusion in the perception of self motion

ion and concretization could also be performed with respect to other parameters, not only spatial location. For example the mechanisms for saccade target position (LIP, FEF, superior SC) are separated from mechanisms that are responsible for saccade execution timing (basal ganglia). One could say that the spatial representation of a saccade target is abstracted from its timing, and vice versa. Neurons clearly have the ability to differentiate and integrate – take for example the typical center-surround receptive fields of retinal ganglion cells, which represent the first derivative (in space or time, or both) of brightness or color, and abstract from absolute brightness or color. On the other hand neurons can also integrate (combine) evidence from several sources to estimate a target value – for example, if an edge is detected from a set of aligned border contrast measurements. Thinking of abstraction as similar to mathematical differentiation and of concretization as similar to mathematical integration might be less far-fetched than it seems. When differentiating a polynomial, the constant value is removed from the formula (the result ’is abstracted from’ the constant, or generalizes over the constant values). During integration, a constant summand has to be provided so that a unique formula can be calculated. It appears that the brain uses this 3.14. ABSTRACTION AND CONCRETIZATION 95 fundamental mathematical property for its computations. This is of course not the only way in which abstractions can be computed. For example, selective attention can also be interpreted as a form of abstraction, since it abstracts from the parts of the sensory context which are not attended. This function is clearly not a simple differentiation of the sensory signals. Also in artificial intelligence, abstraction is an important topic because it helps to reduce computational complexity (for an overview see [Zucker, 2003]). 3.14.2 Abstraction and concretization in neural information representation There are at least three different possibilities how information can be encoded in neural signals. Firstly, the identity of the neuron is important (which neuron or group of neurons is firing; ”population code”). Second, the firing rate of the neuron can carry information (”rate code”). Third, the exact timing of spikesmight be of importance (”temporal coding”) [Panzeri et al., 2001], [Stein et al., 2005]. The brain can probably transform information from one code to another. For example, a rate code can be converted to a precise temporal code by theta oscillations [Mehta et al., 2002], or a population code to a rate code by specific connection patterns between neurons [Groh, 2001]. Cerebellar circuitry might be critical for transforming a population code to a temporal code. There are neural mechanisms for abstraction and concretization with respect to all three information codes. Abstraction could be computed by: • Identity: Convergence of several fibers on a single neuron, which fires similar to a logical OR operation (for example the circuit which has been proposed to be capable of computing V1 ”complex cell” receptive fields from V1 ”simple cell” responses). • Firing rate: The abstraction from absolute firing rate could be performed if an target neuron is close to activation threshold (and thus starts firing already for a few incoming spikes), and has a long refractory period, or is inhibited in regular intervals, which will limit the maximum spike rate of the target neuron. • Exact spike timing: Neuronswhich remember excitation over a long period of time can do this abstraction. Integrate-and-fire neurons also clearly abstract from the exact spike timing of most of the incoming spikes. Concretization could be performed by: • Identity: Convergence of several fibers on a single neuron, which fires similar to a logical AND operation (see for example the models proposed by [Pouget and Snyder, 2000] for coordinate transformations, section 5.4). This principle is also called gain field modulation. 96 CHAPTER 3. CORTICAL AND SUBCORTICAL MECHANISMS • Firing rate: The firing rate produced by a neuron as a response to some synaptic input depends on the intracellular polarization. If the cell potential is close to threshold, incoming spikes will have a strong influence on firing rate, whereas a neuron which is hyperpolarized will not react to the same amount of incoming spikes. • Exact spike timing: Neurons are able to perform temporal AND-like combination of inputs – the neuron fires only if inputs from several sources deliver spikes at exactly the same time. Purkinje cells in the cerebellum are an example, but also pyramidal cells which burst at cooccurrence of apical and basal input [Larkum et al., 1999]. 3.14.3 Abstraction and information conservation Information conservation is an important and often neglected constraint for data processing in the cortex. Important information should not be lost by the generalization process, because it might be needed later. For example, when the brain computes a representation of an object independently of its absolute position in the visual field, it generalizes from this absolute position, which means that the result does not contain this information any more. If the position information was lost, the brain could not act spatially correct on the object. It is necessary that this information is stored somewhere for later use (during concretization). For the processing of the identity and location of visual objects, it is assumed that the information is split in two streams processing identity and spatial information of objects respectively. Whereas responses of neurons in the ’ventral visual stream’ are selective to object identity, they are relatively independent of the absolute position of the object. The position information is stored in the parietal lobe, particularly in areas in the intraparietal sulcus (’dorsal stream’). There are projections from these areas to the motor cortex, where the spatial signals could be used for spatially concretizing actions on objects (for example for grasping). Lesions of the critical regions in parietal cortex lead to specific deficits in spatial aspects of actions on visual targets (see also section 3.6.1). Models for splitting of visual information in location and identity have for example been proposed by [Kosslyn, 1994], [Rolls and Deco, 2002], and [Rao, 2005].