Complex-cell receptive field models

The visual system provides with relevant information to create an internal representation of the environment and with this information to make decisions. Visual information is primarily processed in the visual cortex, where neurons react to certain visual features. In computational neuroscience and artificial vision, the study and modeling of vision processes is a topic of great interest since the human visual system can process a great diversity of stimuli in a wide variety of conditions.

In this work, we propose a computational framework inspired by the human visual system, that integrates models obtained from neuroscience to describe aspects of vision such as color processing and shape processing and thus contribute to formulating a general vision system and incorporating it into artificial entities in order to approximate human behavior.

This system covers the early stages of visual sensory processing, in addition to intermediate processing stages, and considers connections with other cognitive functions within a cognitive architecture. In this proposal, the model is formally described, and the results obtained are analyzed qualitatively to later weigh the considerations for the expansion of this framework.

An important issue for neurophysiological studies of the visual system is the definition of the region of the visual field that can modify a neuron's activity (i.e., the neuron's receptive field – RF). Usually a trade-off exists between precision and the time required to map a RF. Manual methods (qualitative) are fast but impose a variable degree of imprecision, while quantitative methods are more precise but usually require more time. We describe a rapid quantitative method for mapping visual RFs that is derived from computerized tomography and named back-projection. This method finds the intersection of responsive regions of the visual field based on spike density functions that are generated over time in response to long bars moving in different directions. An algorithm corrects the response profiles for latencies and allows for the conversion of the time domain into a 2D-space domain. The final product is an RF map that shows the distribution of the neuronal activity in visual–spatial coordinates. In addition to mapping the RF, this method also provides functional properties, such as latency, orientation and direction preference indexes. This method exhibits the following beneficial properties: (a) speed; (b) ease of implementation; (c) precise RF localization; (d) sensitivity (this method can map RFs based on few responses); (e) reliability (this method provides consistent information about RF shapes and sizes, which will allow for comparative studies); (f) comprehensiveness (this method can scan for RFs over an extensive area of the visual field); (g) informativeness (it provides functional quantitative data about the RF); and (h) usefulness (this method can map RFs in regions without direct retinal inputs, such as the cortical representations of the optic disc and of retinal lesions, which should allow for studies of functional connectivity, reorganization and neural plasticity). Furthermore, our method allows for precise mapping of RFs in a 30° by 30° area of the visual field for an array of microelectrodes of any size in less than 6 min.

Probability distributions of macaque complex cell responses to a large set of images were determined. Measures of selectivity were based on the overall shape of the response probability distribution, as quantified by either kurtosis or entropy. We call this non-parametric selectivity, in contrast to parametric selectivity, which measures tuning curve bandwidths. To examine how receptive field properties affected non-parametric selectivity, two models of complex cells were created. One was a standard Gabor energy model, and the other a slight variant constructed from a Gabor function and its Hilbert transform. Functionally, these models differed primarily in the size of their DC responses. The Hilbert model produced higher selectivities than the Gabor model, with the two models bracketing the data from above and below. Thus we see that tiny changes in the receptive field profiles can lead to major changes in selectivity. While selectivity looks at the response distribution of a single neuron across a set of stimuli, sparseness looks at the response distribution of a population of neurons to a single stimulus. In the model, we found that on average the sparseness of a population was equal to the selectivity of cells comprising that population, a property we call ergodicity. We raise the possibility that high sparseness is the result of distortions in the shape of response distributions caused by non-linear, information-losing transforms, unrelated to information theoretic issues of efficient coding.

Primate’s primary visual cortex (V1) is dominated by complex cells. This choice of nature seems puzzling, as complex cells are insensitive to spatial phase––information which is generally believed to be essential for perceptual characterization and recognition of images. Modeling complex cells as Gabor wavelet magnitudes, we have mathematically and empirically examined the information content of their responses. Our results show that in spite of phase insensitivity of individual complex cell responses, population responses contain sufficient information to capture the perceptual essence of images. A complex cell type representation seems to be not only sufficiently discriminating for object identification, but also––due to its inherent ambiguities––robust to changes in background, lighting, and small deformations.

In primary visual cortex, neurons are classified into simple cells and complex cells based on their response properties. Although the role of these two cell types in vision is still unknown, an attractive hypothesis is that simple cells are necessary to construct complex receptive fields. This hierarchical model puts forward two main predictions. First, simple cells should connect monosynaptically to complex cells. Second, complex cells should become silent when simple cells are inactivated. We have recently provided evidence for the first prediction, and here we do the same for the second. In summary, our results suggest that the receptive fields of most layer 2+3 complex cells are generated by a mechanism that requires simple cell inputs.