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Color perception relies on comparisons between adjacent lights, but how the brain performs these comparisons is poorly understood. To elucidate the underlying mechanisms, we recorded spiking responses of individual V1 neurons in macaque monkeys to pairs of stimuli within the classical receptive field (RF). We estimated the spatial-chromatic RF of each neuron and then presented customized colored edges using a closed-loop technique. We found that many double-opponent (DO) cells, which have spatially and chromatically opponent RFs, responded to chromatic contrast as a weighted sum, akin to how other V1 neurons responded to luminance contrast. Yet other neurons integrated chromatic signals nonlinearly, confirming that linear signal integration is not an obligate property of V1 neurons. The functional similarity of cone-opponent DO cells and cone non-opponent simple cells suggests that these two groups may share a common underlying circuitry, promotes the construction of image-computable models for full-color image representation, and sheds new light on V1 complex cells.

This paper presents an in-depth theoretical analysis of the orientation selectivity properties of simple cells and complex cells, that can be well modelled by the generalized Gaussian derivative model for visual receptive fields, with the purely spatial component of the receptive fields determined by oriented affine Gaussian derivatives for different orders of spatial differentiation. A detailed mathematical analysis is presented for the three different cases of either: (i) purely spatial receptive fields, (ii) space-time separable spatio-temporal receptive fields and (iii) velocity-adapted spatio-temporal receptive fields. Closed-form theoretical expressions for the orientation selectivity curves for idealized models of simple and complex cells are derived for all these main cases, and it is shown that the orientation selectivity of the receptive fields becomes more narrow, as a scale parameter ratio κ , defined as the ratio between the scale parameters in the directions perpendicular to vs. parallel with the preferred orientation of the receptive field, increases. It is also shown that the orientation selectivity becomes more narrow with increasing order of spatial differentiation in the underlying affine Gaussian derivative operators over the spatial domain. A corresponding theoretical orientation selectivity analysis is also presented for purely spatial receptive fields according to an affine Gabor model, showing that: (i) the orientation selectivity becomes more narrow when making the receptive fields wider in the direction perpendicular to the preferred orientation of the receptive field; while (ii) an additional degree of freedom in the affine Gabor model does, however, also strongly affect the orientation selectivity properties.

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system , given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i)  covariance properties under scale changes, affine image deformations, and Galilean transformations of space–time as occur for real-world image data as well as specific requirements of (ii)  temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales . It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision . Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space–time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space–time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically , as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.

When observing the surface patterns of objects delimited by smooth surfaces, the projections of the surface patterns to the image domain will be subject to substantial variabilities, as induced by variabilities in the geometric viewing conditions, and as generated by either monocular or binocular imaging conditions, or by relative motions between the object and the observer over time. To first order of approximation, the image deformations of such projected surface patterns can be modelled as local linearizations in terms of local 2-D spatial affine transformations. This paper presents a theoretical analysis of relationships between the degrees of freedom in 2-D spatial affine image transformations and the degrees of freedom in the affine Gaussian derivative model for visual receptive fields. For this purpose, we first describe a canonical decomposition of 2-D affine transformations on a product form, closely related to a singular value decomposition, while in closed form, and which reveals the degrees of freedom in terms of (i) uniform scaling transformations, (ii) an overall amount of global rotation, (iii) a complementary non-uniform scaling transformation and (iv) a relative normalization to a preferred symmetry orientation in the image domain. Then, we show how these degrees of freedom relate to the degrees of freedom in the affine Gaussian derivative model. Finally, we use these theoretical results to consider whether we could regard the biological receptive fields in the primary visual cortex of higher mammals as being able to span the degrees of freedom of 2-D spatial affine transformations, based on interpretations of existing neurophysiological experimental results.

Simple cells in primary visual cortex are believed to extract local contour information from a visual scene. The 2D Gabor function (GF) model has gained particular popularity as a computational model of a simple cell. However, it short-cuts the LGN, it cannot reproduce a number of properties of real simple cells, and its effectiveness in contour detection tasks has never been compared with the effectiveness of alternative models. We propose a computational model that uses as afferent inputs the responses of model LGN cells with center–surround receptive fields (RFs) and we refer to it as a Combination of Receptive Fields (CORF) model. We use shifted gratings as test stimuli and simulated reverse correlation to explore the nature of the proposed model. We study its behavior regarding the effect of contrast on its response and orientation bandwidth as well as the effect of an orthogonal mask on the response to an optimally oriented stimulus. We also evaluate and compare the performances of the CORF and GF models regarding contour detection, using two public data sets of images of natural scenes with associated contour ground truths. The RF map of the proposed CORF model, determined with simulated reverse correlation, can be divided in elongated excitatory and inhibitory regions typical of simple cells. The modulated response to shifted gratings that this model shows is also characteristic of a simple cell. Furthermore, the CORF model exhibits cross orientation suppression, contrast invariant orientation tuning and response saturation. These properties are observed in real simple cells, but are not possessed by the GF model. The proposed CORF model outperforms the GF model in contour detection with high statistical confidence (RuG data set: p  < 10 −4 , and Berkeley data set: p  < 10 −4 ). The proposed CORF model is more realistic than the GF model and is more effective in contour detection, which is assumed to be the primary biological role of simple cells.

Corner detection is a fundamental task in computer vision that plays a critical role in applications such as image registration, 3D reconstruction, and object tracking. In biological visual systems, simple cells in the primary visual cortex exhibit high selectivity to edge stimuli of specific orientations, while end-stopped cells can detect geometric singular structures such as line segment endpoints and corners. Existing corner detection methods based on visual neural computation typically employ a strategy of densely distributed end-stopped cells for corner localization, which suffers from significant localization deviation under small angle conditions due to mutual interference between responses of adjacent neurons. To address this problem, this paper proposes a bionic corner detection method based on cooperative processing of simple cells and end-stopped cells. The method constructs a two-stage cooperative processing framework: the edge filtering stage employs a Gabor filter bank to simulate the orientation selectivity of simple cells, extracting edge positions and orientation information; the dynamic construction stage builds unilateral end-stopped cells only at filtered edge positions based on local orientation information, fundamentally avoiding computational redundancy and response interference caused by global dense distribution; the corner localization stage determines precise corner coordinates through hierarchical clustering and dual-cluster centroid fusion strategies. Experimental results demonstrate that, in the 15° acute-angle regime where dense end-stopped schemes are most severely affected by response interference, the proposed method reduces the mean localization error from 8.76 to 2.34 pixels, corresponding to a 73.3% improvement; averaged across the eight tested angle levels from 15° to 165°, the improvement is approximately 40.9%, and all per-angle differences are statistically significant (paired t-test, p < 0.01 or below, N = 10 independent runs). On standard test images, the method attains the lowest mean localization error among the eight compared detectors (1.58 pixels, versus 1.68–3.42 pixels for Harris, FAST, COSFIRE, KAZE, SuperPoint, Deep Corner, and Wei et al.), while maintaining competitive detection rate, false-alarm rate, and runtime. Physiological plausibility validation experiments show that the correlation coefficient between the detection deviation of this method and human perceptual deviation reaches 0.923, indicating that the output of the framework aligns with previously reported human perceptual bias patterns and supporting its biological plausibility as a biologically inspired—rather than mechanistic—model of corner perception. The source code, dataset, and experimental results are publicly available (see Data Availability Statement).

This article examines the problems of multi-robot coverage and persistent monitoring of regions of interest with limited sensing robots. A group of robots, each equipped with only contact sensors and a clock, execute a simple trajectory by repeatedly moving straight and then bouncing at perimeter boundaries by rotating in place. We introduce an approach by finding a joint trajectory for multiple robots to cover a given environment and generating cycles for the robots to persistently monitor the target regions in the environment. From a given initial configuration, our approach iteratively finds the joint trajectory of all the robots that covers the entire environment. Our approach also computes periodic trajectories of all the robots for monitoring of some regions, where trajectories overlap but do not involve robot-robot collisions. We present experimental results from multiple simulations and physical experiments demonstrating the practical utility of our approach.

In this paper, we study the multi-objective optimization of the viscous boundary condition of an elastic rod using a hybrid method combining a genetic algorithm and simple cell mapping (GA-SCM). The method proceeds with the NSGAII algorithm to seek a rough Pareto set, followed by a local recovery process based on one-step simple cell mapping to complete the branch of the Pareto set. To accelerate computation, the rod response under impulsive loading is calculated with a particular solution method that provides accurate structural responses with less computational effort. The Pareto set and Pareto front of a case study are obtained with the GA-SCM hybrid method. Optimal designs of each objective function are illustrated through numerical simulations.

The origin of orientation selectivity in the responses of simple cells in cat visual cortex serves as a model problem for understanding cortical circuitry and computation. The feed-forward model posits that this selectivity arises simply from the arrangement of thalamic inputs to a simple cell. Much evidence, including a number of recent intracellular studies, supports a primary role of the thalamic inputs in determining simple cell response properties, including orientation tuning. This mechanism alone, however, cannot explain the invariance of orientation tuning to changes in stimulus contrast. Simple cells receive push-pull inhibition: ON inhibition in OFF subregions and vice versa. Addition of such inhibition to the feed-forward model can account for this contrast invariance, provided the inhibition is sufficiently strong. The predictions of \"normalization\" and \"feedback\" models are reviewed and compared with the predictions of this modified feed-forward model and with experimental results. The modified feed-forward and the feedback models ascribe fundamentally different functions to cortical processing.

During natural viewing, the eyes are never still. Even during fixation, miniature movements of the eyes move the retinal image across tens of foveal photoreceptors. Most theories of vision implicitly assume that the visual system ignores these movements and somehow overcomes the resulting smearing. However, evidence has accumulated to indicate that fixational eye movements cannot be ignored by the visual system if fine spatial details are to be resolved. We argue that the only way the visual system can achieve its high resolution given its fixational movements is by seeing via these movements. Seeing via eye movements also eliminates the instability of the image, which would be induced by them otherwise. Here we present a hypothesis for vision, in which coarse details are spatially encoded in gaze-related coordinates, and fine spatial details are temporally encoded in relative retinal coordinates. The temporal encoding presented here achieves its highest resolution by encoding along the elongated axes of simple-cell receptive fields and not across these axes as suggested by spatial models of vision. According to our hypothesis, fine details of shape are encoded by inter-receptor temporal phases, texture by instantaneous intra-burst rates of individual receptors, and motion by inter-burst temporal frequencies. We further describe the ability of the visual system to readout the encoded information and recode it internally. We show how reading out of retinal signals can be facilitated by neuronal phase-locked loops (NPLLs), which lock to the retinal jitter; this locking enables recoding of motion information and temporal framing of shape and texture processing. A possible implementation of this locking-and-recoding process by specific thalamocortical loops is suggested. Overall it is suggested that high-acuity vision is based primarily on temporal mechanisms of the sort presented here and low-acuity vision is based primarily on spatial mechanisms.