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The visual area V4 has been considered to play a crucial role in the intermediate representation of objects, where low-level image features are transformed into object-level representations. We estimated the intrinsic dimensionality in V4 for the representation of local patches generated from natural scenes. The dimensionality was approximately 40, which is approximately half of that reported in IT for the representation of whole natural objects. The analyses of the estimated dimensionality suggest both common and independent representations that code contour shapes and/or surfaces with textures, implying a relatively complex and mixed representation in the intermediate-level area.

Figure-ground (FG) segregation has been considered as a fundamental step towards object recognition. We explored plausible mechanisms that estimate global figure-ground segregation from local image features by investigating the human visual system. Physiological studies have reported border-ownership (BO) selective neurons in V2 which signal the local direction of figure (DOF) along a border; however, how local BO signals contribute to global FG segregation has not been clarified. The BO and FG processing could be independent, dependent on each other, or inseparable. The investigation on the differences and similarities between the BO and FG judgements is important for exploring plausible mechanisms that enable global FG estimation from local clues. We performed psychophysical experiments that included two different tasks each of which focused on the judgement of either BO or FG. The perceptual judgments showed consistency between the BO and FG determination while a longer distance in gaze movement was observed in FG segregation than BO discrimination. These results suggest the involvement of distinct neural mechanism for local BO determination and global FG segregation.

In this paper we propose a method for constructing a Gray map for a group. In an earlier paper, we suggested a new design principle of Gray maps for groups and tried to apply it to several concrete groups. Though the trial had some success, the method is not very constructive. In this paper we try to design a more constructive method based on the semidirect-product structure of the target group.

In this paper we propose a new construction method of Gray maps for groups. In a earlier paper, we succeeded the Type 1 construction for all groups of order 16 and confirmed that we can construct Type 2 maps for several groups of order 16, but failed to construct such maps for other groups. Therefore, in this paper we try to apply the new construction method to them.

In this paper, we study a combination (called the generalized cyclic Nimhoff) of the cyclic Nimhoff and subtraction games. We give the $\mathscr{G}$-value of the game when all the $\mathscr{G}$-value sequences of the component subtraction games have a common $h$-stair structure.

The symmetry axis is the midline that divides a pattern into congruent halves, which is physically nonexistent but evokes tilt aftereffect (TAE). To investigate the cortical correspondence of the symmetry axis, we examined the invariance of symmetry-induced TAE with regard to low-level visual features and the spatial transfer of TAE over visual fields. When the adaptation pattern was rotated and changed sequentially with the orientation of the symmetry axis unchanged, the measured TAE decreased only slightly (18%) compared to stationary patterns. This effect persisted when the adaptation and test patterns were presented in different visual fields. These results indicate that the cortical representation of symmetry is generated independently of low-level features and involves higher-level visual areas.

We investigated whether specular highlights facilitate the perception of shape from shading in a search paradigm and how highlights interact with shading to facilitate this perception. Our results indicated that stimuli containing highlights led to shorter searching time with the dependence on the light source direction (top lights make searching faster), suggesting that highlights indeed facilitate shape-from-shading processing. To examine how highlight processing interacts with shading processing, we tested unnatural stimuli for which the lighting directions for shading and highlights were inconsistent. The results indicated that unnatural highlights (bright spots) placed in a direction inconsistent with the shading either decrease or do not alter searching time. This suggests that highlights may facilitate, and not suppress, shading processing. With more physically plausible highlights generated from image-based lighting, we also observed facilitation with consistent highlights, but no change with inconsistent highlights. Finally, we examined whether highlights indeed work to facilitate depth perception in a discrimination task. The results showed that correct discrimination of depth increases when highlights are added to shading even when their lighting directions are inconsistent. These results indicate that specular highlights facilitate shading processing, and do not suppress it even when the highlights are placed in a direction inconsistent with shading. The results also elucidate the lighting constraints of the visual system.

The perceptual constancy of shape, including view invariance, is an amazing property of the visual system. Cortical representation by the medial axis (MA) is an attractive candidate for maintaining the constancy of a wide range of arbitrary shapes. Recent physiological studies have reported that neurons in the primary visual cortex (V1) show a response to two-dimensional (2D) MAs, and those in the inferior temporal cortex (IT) are selective to three-dimensional (3D) MAs. However, little is known about the neural mechanisms underlying the transformation of 2D to 3D MAs. As a first step toward investigating the cortical mechanism, we have proposed as a hypothesis that a pair of monocular 2D MAs is fused to generate a 3D MA. We examined the computational plausibility of the hypothesis; specifically, whether an energy-based fusion model is capable of generating 3D MAs. We generated blob-like, physiologically plausible 2D MAs, and used a standard energy model to detect the disparity between a pair of 2D MAs. The model successfully generated 3D MAs for a variety of objects that included typical shape characteristics. A reconstruction test showed that the computed 3D MAs captured the essential structure of the objects with reasonable accuracy and view invariance. These results indicate that the fusion of monocular blob-like 2D MAs is capable of generating a reasonable 3D MA within the framework of the energy model.

Border ownership (BO) indicates which side of a contour owns a border, and it plays a fundamental role in figure-ground segregation. The majority of neurons in V2 and V4 areas of monkeys exhibit BO selectivity. A physiological work reported that the responses of BO-selective cells show a rapid transition when a presented square is flipped along its classical receptive field (CRF) so that the opposite BO is presented, whereas the transition is significantly slower when a square with a clear BO is replaced by an ambiguous edge, e.g., when the square is enlarged greatly. The rapid transition seemed to reflect the influence of feedforward processing on BO selectivity. Herein, we investigated the role of feedforward signals and cortical interactions for time-courses in BO-selective cells by modeling a visual cortical network comprising V1, V2, and posterior parietal (PP) modules. In our computational model, the recurrent pathways among these modules gradually established the visual progress and the BO assignments. Feedforward inputs mainly determined the activities of these modules. Surrounding suppression/facilitation of early-level areas modulates the activities of V2 cells to provide BO signals. Weak feedback signals from the PP module enhanced the contrast gain extracted in V1, which underlies the attentional modulation of BO signals. Model simulations exhibited time-courses depending on the BO ambiguity, which were caused by the integration delay of V1 and V2 cells and the local inhibition therein given the difference in input stimulus. However, our model did not fully explain the characteristics of crucially slow transition: the responses of BO-selective physiological cells indicated the persistent activation several times longer than that of our model after the replacement with the ambiguous edge. Furthermore, the time-course of BO-selective model cells replicated the attentional modulation of response time in human psychophysical experiments. These attentional modulations for time-courses were induced by selective enhancement of early-level features due to interactions between V1 and PP. Our proposed model suggests fundamental roles of surrounding suppression/facilitation based on feedforward inputs as well as the interactions between early and parietal visual areas with respect to the ambiguity dependence of the neural dynamics in intermediate-level vision.

The cortical area V4 produces a representation of curvature as the intermediate-level representation of an object's shape. We investigated whether sparse coding is the principle driving the generation of the spatial properties of the receptive field in V4 that exhibit curvature selectivity. To investigate the role of sparseness in the construction of curvature representations, we applied component analysis with a sparseness constraint to the activity of model V2 neurons that were responding to shapes derived from natural images. Our simulation results showed that single basis functions with medium degrees of sparseness (0.7-0.8) produced curvature selectivity, and their population activity produced acute curvature bias. The results support the hypothesis that sparseness plays an essential role in the construction of curvature selectivity in V4.

Perception of the material quality of a surface depends on its reflectance properties. Recent physiological studies reported the neural selectivity to glossy surfaces in the Inferior Temporal cortical areas [e.g., 1]. In the present study, we examine the hypothesis that basis neurons are selective to typical materials, and that the combinations of their responses are representative of a variety of natural materials. To assess the hypotheses, we performed a psychological experiment based on adaptation. If adaptation to a specific material is observed, the presence of neurons that are selective to the specific material is predicted. We performed adaptation tests with six typical material qualities including gloss, matte, metal and wood. We observed the adaptation to certain materials but not to some other materials. This result indicates the presence of basis neurons that are selective to materials, which is fundamentally important for understanding cortical representation of surface materials.

Figure-ground (FG) segregation is a crucial function of the intermediate-level vision. Physiological studies on monkey V2 have reported border-ownership (BO) selective cells that signal the direction of figure along a local border. However, local borders in natural images are often complicated and they often do not provide a clue for FG segregation. In the present study, we hypothesize that a population of V4 cells represents FG by means of surface rather than border. We investigated this hypothesis by the computational analysis of neural signals from multiple cells in monkey V4. Specifically, we applied Support Vector Machine as an ideal integrator to the cellular responses, and examined whether the responses carry information capable of determining correct local FG. Our results showed that the responses from several tens of cells are capable of determining correct local FG in a variety of natural image patches while single-cell responses hardly determine FG, suggesting a population coding of local FG by a small number of cells in V4.

We investigated computationally the role of V1 complex cells in the simultaneous determination of depth and motion, in conjunction with spatiotemporal response characteristics of the cells. First, we examined whether a pooling of simple-cell units with monocular, spatiotemporal response profiles evokes binocular, spatiotemporal response profiles of complex cells. Second, we examined whether a population of the cascade complex-cell models yields the responses being consistent with the perception of depth and motion. We tested various stimuli including ambiguous cases that consist of interocular time delay without spatial disparity. Our simulation study showed that a pooling of simple cells leads to the generation of binocular response profiles of complex cells, and that a population of the complex cells provides a basis for the simultaneous perception of depth and motion.

Many neurons in monkeys' V2 and V4 are selective for border ownership (BO) [H. Zhou, H.S. Friedman, R. von der Heydt, Coding of border ownership in monkey visual cortex, J. Neurosci. 20 (2000) 6594-6611). We have developed a computational model for the BO determination of the neurons based on their contextual modulation. Our model consists of hundreds of model cells with distinct surround suppressive/facilitatory regions that are generated by a linear combination of Gaussians. The simulation results show that many model cells realize the major characteristics of BO selective neurons. Investigating the surrounding regions of the BO selective model cells with perfect consistency, we found that their iso orientation suppression is dominant over the cross orientation facilitation, which agrees quantitatively with physiological reports. These results suggest that the surrounding modulation is a fundamental mechanism for BO selectivity.

A recent physiological finding of neural coding for border ownership (BO) that defines the direction of a figure with respect to the border has provided a possible basis for figure-ground segregation. To explore the underlying neural mechanisms of BO, we investigated stimulus configurations that activate BO circuitry through psychophysical investigation of the BO-dependent tilt aftereffect (BO-TAE). Specifically, we examined robustness of the border ownership signal by determining whether the BO-TAE is observed when gestalt factors are broken. The results showed significant BO-TAEs even when a global shape was not explicitly given due to the ambiguity of the contour, suggesting a contour-independent mechanism for BO coding., This paper was published in Journal of the Optical Society of America. A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=josaa-24-1-18. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Contextual modulation reported in early- to intermediate-level visual areas could be an essential component to signal border ownership (BO) that specifies the direction of figure along a contour. The surrounding regions that evoke significant suppression or facilitation are highly localized and asymmetric with respect to the center of the classical receptive field (CRF). We propose a hypothesis that such surrounding modulation is a basis for BO-selectivity. Although this idea has been discussed for several years, it is uncertain how many of a vast variety of surrounding organizations could signal correctly the direction of ownership, and how many could signal consistently for various stimuli. We carried out computationally a population study of the surrounding effects to investigate how many cells exhibit effective and consistent BO signals. We tested hundreds of various organizations, and found that most of the asymmetric, iso-orientation suppressive regions, regardless of position or size, lead to surprisingly high consistency in the direction of ownership for various stimuli. The combinations of iso-orientation suppression and cross-orientation facilitation indicate both high robustness and consistency in the ownership determination. We constructed a model for BO-selective neurons based on the surrounding effects, and investigated whether the model reproduces major characteristics of the neuronal responses, including a variety in the BO selectivity among neurons, consistency with respect to various stimuli, invariance to stimulus size, and co-selectivity to BO and contrast. The model reproduced successfully the major characteristics of BO-selective neurons.

For analyzing impartial games played in the misere rule, Yamasaki defined flatness of games, while Conway defined tameness. In this paper, we prove that these two concepts are equivalent.

We have proposed the computational model for border-ownership (BO) determination based on the contrast configurations within a certain range that extends beyond the classical receptive field (CRF). In this study, we adopt two crucial functions of the surrounding modulation reported by the recent physiological studies; (1) changes in functional connection depending on the amplitude of contrast, and (2) a variety of surrounding suppression/facilitation depending on the orientation and retinotopic position of surrounding stimuli relative to the CRF. Simulation results show that the model reproduces the major characteristics of BO selective neurons.

We investigate the neural mechanisms for border-ownership (BO) determination, specifically whether the determination of BO is plausible from the contrast configuration within a certain range that extends beyond the classical receptive fields. The relevance of the contrast is suggested since the majority of BO-selective neurons in V2 and V4 show co-selectivity to the contrast. We hypothesize that the spatial structure of surrounding inhibition/excitation recently revealed in V1, or the similar structure in V2, is a key to integrate surrounding contrast to determine BO. The model reproduces a range of the neuronal activities responding to complex figures including occlusion.

Figure-ground FG segregation is a crucial function of the intermediate-level vision. Physiological studies have suggested that monkey V4 cells are sensitive to FG organization, although their selectivity to FG and what they represent have not been clarified. We investigated computationally whether a subpopulation of cells in V4 represents FG. Specifically, we applied support vector machine to the responses of 1---100 cells to natural-image patches that were recorded from V4 of two macaque monkeys Macaca fuscata by multi-electrode arrays. Our results showed that the responses of a group of cells were capable of segregating FG while the responses of single-cells were not, suggesting a distributed representation of FG in V4.

We investigate which neural grouping is relevant to the perception of the global orientations of bars. We examine psychophysically whether perceptual segmentation affects the apparent tilt in X-shaped junctions constructed by solid or illusory bars. The results show that perceptual segmentation is not relevant to the global orientation, except for illusory stimuli. Early level processing, probably in the primary visual cortex (V1), seems to be involved in the determination of global orientation. We propose a network model consisting of V1 neurons and a grouping mechanism which synchronizes the cellular activities based on colinear coupling. The computed bar orientations agree quantitatively with the apparent tilt measured in comparable psychophysical experiments reported elsewhere.

We investigate what computational mechanisms give rise to the nonlinearity of complex cell responses in the primary visual cortex. Complex cells are characterized by their nonlinear spatial properties such as spatial phase invariance and nonlinear spatial additivity. We carried out network simulations to estimate the second-order Wiener-like kernels for several different models. Models with nonlinear spatial pooling of simple-cell-like linear subunits reproduce the second-order kernels in good agreement with physiologically estimated kernels, while models without the pooling mechanism fail to reproduce the kernel. The results support the cascade mechanism consisting of simple cells’ local feature extraction followed by spatial pooling.

We propose a network model for explaining tilt illusion based on a V1 circuit preserving retinotopy and a mechanism for grouping neuronal activities. The simulation of the model indicates that many V1 neurons show responses which correspond to the tilt effects, depending on the geometric configuration of the local visual pattern projected on to the receptive field of the neuron. Grouping V1 neurons based on the segmentation suggested by our psychophysical experiments, the model reproduces the apparent orientations of the bars in good quantitative agreement with the results of comparable psychophysical experiments reported elsewhere.

Symmetry has long been considered as an influential Gestalt factor for grouping and figure-ground segregation. As natural contours are not precisely symmetric in terms of geometry, we proposed a quantification of the degree of symmetry (DoS) that is applicable for arbitrary contours in natural images. DoS showed an agreement with the perception of symmetry in judgment of symmetry axis. Multi-dimensional scaling, together with similarity tests among natural contours, showed that DoS is a quantitative perceptual measure that accounts for the shape of contour. These results indicate that DoS reflects the perception of symmetry in natural contours, and further suggest that DoS is a plausible candidate for representing shape in the cortex.

We describe a neural simulator designed for simulating very large scale models of cortical architectures. This simulator, NEXUS, uses coarse-grain parallel computing by distributing computation and data onto multiple conventional workstations connected via a local area network. Coarse-grain parallel computing offers natural advantages in simulating functionally segregated neural processes. We partition a complete model into modules with locally dense connections—a module may represent a cortical area, column, layer, or functional entily. Asynchronous data communications among workstations are established through the Network File System, which, together with the implicit modularity, decreases communications overhead, and increases overall performance. Coarse-grain parallelism also benefits from the standardization of conventional workstations and LAN, including portability between generations and vendors.

We investigate the psychophysical and computational processes underlying the perception of depth from texture cues in perspective projections. In particular, we analyse the similarities between the processes associated with perspective and orthographic projections. Based on a series of psychophysical experiments using white noise stimuli presented in perspective projection, we suggest that the visual system may characterize the spatial-frequency spectrum by the average peak frequency (APF), which is the same characteristic as that used in orthographic projections. We demonstrate that normalization of the APF yields an estimate of depth in perspective projection. Our previous studies suggest that the APF is used in orthographic projections, where the output of the normalization process represents a linear approximation of surface slant. Based on these results, together with previous psychophysical evidence, we propose a neural network model of shape-from-texture for the perspective view. Simulations of the...

Directing attention to the spatial location or the distinguishing feature of a visual object modulates neuronal responses in the visual cortex and the stimulus discriminability of subjects. However, the spatial and feature-based modes of attention differently influence visual processing by changing the tuning properties of neurons. Intriguingly, neurons' tuning curves are modulated similarly across different visual areas under both these modes of attention. Here, we explored the mechanism underlying the effects of these two modes of visual attention on the orientation selectivity of visual cortical neurons. To do this, we developed a layered microcircuit model. This model describes multiple orientation-specific microcircuits sharing their receptive fields and consisting of layers 2/3, 4, 5, and 6. These microcircuits represent a functional grouping of cortical neurons and mutually interact via lateral inhibition and excitatory connections between groups with similar selectivity. The individual microcircuits receive bottom-up visual stimuli and top-down attention in different layers. A crucial assumption of the model is that feature-based attention activates orientation-specific microcircuits for the relevant feature selectively, whereas spatial attention activates all microcircuits homogeneously, irrespective of their orientation selectivity. Consequently, our model simultaneously accounts for the multiplicative scaling of neuronal responses in spatial attention and the additive modulations of orientation tuning curves in feature-based attention, which have been observed widely in various visual cortical areas. Simulations of the model predict contrasting differences between excitatory and inhibitory neurons in the two modes of attentional modulations. Furthermore, the model replicates the modulation of the psychophysical discriminability of visual stimuli in the presence of external noise. Our layered model with a biologically suggested laminar structure describes the basic circuit mechanism underlying the attention-mode specific modulations of neuronal responses and visual perception.

Physiological studies have reported that the intermediate-level visual area represents primitive shape by the selectivity to curvature and its direction. However, it has not been revealed that what coding scheme underlies the construction of the selectivity with complex characteristics. We propose that sparse representation is crucial for the construction so that a sole control of sparseness is capable of generating physiological characteristics. To test the proposal, we applied component analysis with sparseness constraint to activities of model neurons, and investigated whether the computed bases reproduce the characteristics of the selectivity. To evaluate the learned bases quantitatively, we computed the tuning properties of single bases and the population, as similar to the physiological reports. The basis functions reproduced the physiological characteristics when sparseness was medium (0.6-0.8). These results indicate that sparse representation is crucial for the curvature selectivity, and that a sole control of sparseness is capable of constructing the representation.

Border Ownership (BO) selective cells show complex behavior in latency, such as a shorter latency for a farther figural element. The complex behavior of latency would give crucial constraints for understanding the neuronal mechanisms underlying BO selectivity. We propose that the delays in the feed-forward mechanisms of surround modulation account for the characteristics of the latency. Specifically, combinations of delays between V1 cells, surround center and BO-selective cells underlie the latency characteristics. To examine the hypothesis, we constructed the V1-V2 feed-forward model and carried out Monte Carlo simulations with a variety of surround regions. The results indicate that physiologically realistic surround regions reproduce the puzzled behavior of latency. The results support the feed-forward mechanism of surround modulation for the neural mechanism underlying the BO selectivity.

The determination of Border-Ownership (BO) that defines the direction of figure along contour is a crucial step toward figure-ground segregation. Recent physiological and computational studies have reported that neurons in V2/V4 are selective to BO [1], and that surround modulation underlies the selectivity [2, 3]. Accurate determination of BO along complex contours in natural images appears difficult for a single BO-selective cell, leading to the hypothesis that multiple cells work simultaneously for BO perception. We studied computationally how many BO cells and what characteristics of the surround modulation are required to achieve accurate determination of BO in natural images. The results indicated that 10 model BO-cells achieve 82% correct while single model cells yield 65%. The results suggest that grouping a small number of BO-selective cells increases effectively the capability for the determination of BO.

Recent physiological studies have reported that neurons in the cortical area V4 are selective to curvature along object contour. The neurons are capable of discriminating convexity and concavity, and indicating the direction of the curvature with respect to the contour projected onto their cRF. We propose that surface representation plays a crucial role in constructing the selectivity for curvature because convexity/concavity cannot be determined without the construction of object surface. To test the proposal, we developed a computational-model of V1-V4 networks that computes spatiotemporal activities of single cells, and carried out the simulations with the stimuli used by the physiological studies. The model neurons reproduced the selectivity for specific curvature and direction. Population of the model cells showed a bias toward convex curvature as consistent with V4 population in vivo. These results support that the representation of surface is crucial for the construction of the selectivity in V4.

Determination of the figure region in an image is a fundamental step toward surface construction, shape coding, and object representation. Localized, asymmetric surround modulation, reported neurophysiologically in early-to-intermediate-level visual areas, has been proposed as a mechanism for figure-ground segregation. We investigated, computationally, whether such surround modulation is capable of yielding consistent and robust determination of figure side for various stimuli. Our surround modulation model showed a surprisingly high consistency among pseudorandom block stimuli, with greater consistency for stimuli that yielded higher accuracy of, and shorter reaction times in, human perception. Our analyses revealed that the localized, asymmetric organization of surrounds is crucial in the detection of the contrast imbalance that leads to the determination of the direction of figure with respect to the border. The model also exhibited robustness for gray-scaled natural images, with a mean correct rate of 67%, which was similar to that of figure-side determination in human perception through a small window and of machine-vision algorithms based on local processing. These results suggest a crucial role of surround modulation in the local processing of figure-ground segregation.

The border ownership (BO) that indicates which side of the contour owns the border plays a fundamental role in object perception[1]. The responses of BO-selective cells exhibit rapid transition when a stimulus is fliped along its classical receptive field so that the opposite BO is presented, while the transition is significantly slower when a clear BO is turned into an ambiguous edge such as when a square is enlarged extensively[2]. This phenomenon appears to be a crucial clue for understanding the neural mechanims underlying the credibility of BO. We hypothesize that dynamics of BO-selective cells and networks behind them play a crucial role in the credibility, and that the credibility is related to early visual areas as an appearance of a salient object evokes bottom-up attention. To investigate these hypotheses, we examined the dynamics of BO-selective cells with a computational model that include recurent pathways among V1, V2 and Posterior Parietal (PP) areas[3]. The model cells have been shown to reproduce effects of spatial attention. Simulations of the model exhibited distinct response time depending on the ambiguity of BO, indicating a crucial role of dynamics in the credibility. The recurrent network between PP and V1 appear to play a crucial role for the time course of BO-selective cells that governs simultaneously both credibility of BO and bottom-up attention.

Recent physiological studies have reported Border-Ownership (BO) selective cells that signal the direction of figure along a contour, which appear to be a basis for figure-ground segregation. Surround modulation has been proposed as an underlying neural mechanism of BO determination. The crucial question to the model is its orientation specificity: whether BO could be determined only from iso-orientation (with respect to the preferred orientation of the classical receptive field) that has been reported dominant in the modulation. We investigated computationally the dependence of surround modulation on the orientation characteristics during the determination of BO with natural images. The results showed that, even when modulation was limited to iso-orientation, population responses obtained through integration were unchanged while the responses of individual cells were varied, indicating a dominant role of isoorientation suppression and an effectiveness of population coding in BO determination.

There is little understanding on representation and reconstruction of object shape in the cortex. Physiological studies with macaque suggested that neurons in V1 respond to Medial-Axis (MA). We investigated whether (1) early visual areas could provide basis for MA representation, and (2) we could reconstruct the original shape from its MA, with a physiologically realistic computational model consisting of early- to intermediate-level visual areas. Assuming the synchronization of border-ownership selective cells at stimulus onset, our model was capable of detecting MA, indicating that early visual area could provide basis for MA representation. Furthermore, we propose a physiologically plausible reconstruction algorithm with the summation of distinct gaussians.