Computational aspects of motion perception in natural and artificial vision systems.

In this paper a computational scheme for motion perception in artificial and natural vision systems is described. The scheme is motivated by a mathematical analysis in which first-order spatial properties of optical flow, such as singular points and elementary components of optical flow, are shown to be salient features for the computation and analysis of visual motion. The fact that different methods for the computation of optical flow produce similar results is explained in terms of the simple spatial structure of the image motion of rigid bodies. Singular points and elementary flow components are used to compute motion parameters, such as time-to-collision and angular velocity, and also to segment the visual field into areas which correspond to different motions. Then a number of biological implications are discussed. Electrophysiological findings suggest that the brain perceives visual motion by detecting and analysing optical flow components. However, the cortical neurons, which seem to detect elementary flow components, are not able to extract these components from more complex flows. A simple model for the organization of the receptive field of these cells, which is consistent with anatomical and electrophysiological data, is described at the end of the paper.     

Speed tuning in elementary motion detectors of the correlation type

A prominent model of visual motion detection is the so-called correlation or Reichardt detector. Whereas this model can account for many properties of motion vision, from humans to insects (review, Borst and Egelhaaf 1989), it has been commonly assumed that this scheme of motion detection is not well suited to the measurement of image velocity. This is because the commonly used version of the model, which incorporates two unidirectional motion detectors with opposite preferred directions, produces a response which varies not only with the velocity of the image, but also with its spatial structure and contrast. On the other hand, information on image velocity can be crucial in various contexts, and a number of recent behavioural experiments suggest that insects do extract velocity for navigational purposes (review, Srinivasan et al. 1996). Here we show that other versions of the correlation model, which consists of a single unidirectional motion detector or incorporates two oppositely directed detectors with unequal sensitivities, produce responses which vary with image speed and display tuning curves that are substantially independent of the spatial structure of the image. This surprising feature suggests simple strategies of reducing ambiguities in the estimation of speed by using components of neural hardware that are already known to exist in the visual system. Received: 30 April 1998 / Accepted in revised form: 18 September 1998     

Limit cycles of the two-dimensional motion field

Recently, it has been shown that there can be limit cycles in the vector field generated by the perspective projection on the image plane of the three dimensional velocity field of a certain class of non-planar rotating surfaces. In this paper, it is shown that, for any possible rigid motion, there cannot be limit cycles in the motion field of a planar surface. Therefore, the presence of limit cycles in the motion field is necessarily due to the non-planar structure of the viewed scene. An experiment on real images is also presented in which a limit cycle occurs when two planar patches have different orientation in space rotate around a fixed axis.     

The interpretation of a moving retinal image

It is shown that from a monocular view of a rigid, textured, curved surface it is possible, in principle, to determine the gradient of the surface at any point, and the motion of the eye relative to it, from the velocity field of the changing retinal image, and its first and second spatial derivatives. The relevant equations are redundant, thus providing a test of the rigidity assumption. They involve, among other observable quantities, the components of shear of the retinal velocity field, suggesting that the visual system may possess specialized channels for computing these components.     

Mean curvature motion facilitates the segmentation and surface visualization of electron tomograms

Three-dimensional visualization of biological samples is essential for understanding their architecture and function. However, it is often challenging due to the macromolecular crowdedness of the samples and low signal-to-noise ratio of the cryo-electron tomograms. Denoising and segmentation techniques address this challenge by increasing the signal-to-noise ratio and by simplifying the data in images. Here, mean curvature motion is presented as a method that can be applied to segmentation results, created either manually or automatically, to significantly improve both the visual quality and downstream computational handling. Mean curvature motion is a process based on nonlinear anisotropic diffusion that smooths along edges and causes high-curvature features, such as noise, to disappear. In combination with level-set methods for image erosion and dilation, the application of mean curvature motion to electron tomograms and segmentations removes sharp edges or spikes in the visualized surfaces, produces an improved surface quality, and improves overall visualization and interpretation of the three-dimensional images.     

The optical flow of planar surfaces

The human visual system can recover the 3-D shape of moving objects on the basis of motion information alone. Computational studies of this capacity have considered primarily non-planar rigid objects. With respect to moving planar surfaces, previous studies have shown that the planar velocity field has in general a two-fold ambiguity: there are two different planes engaged in different motions that can induce the same velocity field. The current analysis extends the analysis of the planar velocity field in four directions: (1) the use of flow parameters of the type suggested by Koenderink and van Doorn (Optica Acta, 1975, 22, 773-791), (2) the exclusion of confusable non-planar solutions, (3) a new proof and a new method for computing the 3-D motion and surface orientation (4) a comparison with the information available in orthographic velocity fields, which is important for determining the stability of the 3-D recovery process.     

Seeing Circles and Drawing Ellipses: When Sound Biases Reproduction of Visual Motion

The perception and production of biological movements is characterized by the 1/3 power law, a relation linking the curvature and the velocity of an intended action. In particular, motions are perceived and reproduced distorted when their kinematics deviate from this biological law. Whereas most studies dealing with this perceptual-motor relation focused on visual or kinaesthetic modalities in a unimodal context, in this paper we show that auditory dynamics strikingly biases visuomotor processes. Biologically consistent or inconsistent circular visual motions were used in combination with circular or elliptical auditory motions. Auditory motions were synthesized friction sounds mimicking those produced by the friction of the pen on a paper when someone is drawing. Sounds were presented diotically and the auditory motion velocity was evoked through the friction sound timbre variations without any spatial cues. Remarkably, when subjects were asked to reproduce circular visual motion while listening to sounds that evoked elliptical kinematics without seeing their hand, they drew elliptical shapes. Moreover, distortion induced by inconsistent elliptical kinematics in both visual and auditory modalities added up linearly. These results bring to light the substantial role of auditory dynamics in the visuo-motor coupling in a multisensory context.     

The mechanism of interaction between visual flow and eye velocity signals for heading perception

A translating eye receives a radial pattern of motion that is centered on the direction of heading. If the eye is rotating and translating, visual and extraretinal signals help to cancel the rotation and to perceive heading correctly. This involves (1) an interaction between visual and eye movement signals and (2) a motion template stage that analyzes the pattern of visual motion. Early interaction leads to motion templates that integrate head-centered motion signals in the visual field. Integration of retinal motion signals leads to late interaction. Here, we show that retinal flow limits precision of heading. This result argues against an early, vector subtraction type of interaction, but is consistent with a late, gain field type of interaction with eye velocity signals and neurophysiological findings in area MST of the monkey.     

Retinal optic flow during natural locomotion

We examine the structure of the visual motion projected on the retina during natural locomotion in real world environments. Bipedal gait generates a complex, rhythmic pattern of head translation and rotation in space, so without gaze stabilization mechanisms such as the vestibular-ocular-reflex (VOR) a walker’s visually specified heading would vary dramatically throughout the gait cycle. The act of fixation on stable points in the environment nulls image motion at the fovea, resulting in stable patterns of outflow on the retinae centered on the point of fixation. These outflowing patterns retain a higher order structure that is informative about the stabilized trajectory of the eye through space. We measure this structure by applying the curl and divergence operations on the retinal flow velocity vector fields and found features that may be valuable for the control of locomotion. In particular, the sign and magnitude of foveal curl in retinal flow specifies the body’s trajectory relative to the gaze point, while the point of maximum divergence in the retinal flow field specifies the walker’s instantaneous overground velocity/momentum vector in retinotopic coordinates. Assuming that walkers can determine the body position relative to gaze direction, these time-varying retinotopic cues for the body’s momentum could provide a visual control signal for locomotion over complex terrain. In contrast, the temporal variation of the eye-movement-free, head-centered flow fields is large enough to be problematic for use in steering towards a goal. Consideration of optic flow in the context of real-world locomotion therefore suggests a re-evaluation of the role of optic flow in the control of action during natural behavior.     

Motion perception: from phi to omega.

When human observers view dynamic random noise, such as television ''snow'', through a curved or annular aperture, they experience a compelling illusion that the noise is moving smoothly and coherently around the curve (the ''omega effect''). In several series of experiments, we have investigated the conditions under which this effect occurs and the possible mechanisms that might cause it. We contrast the omega effect with ''phi motion'', seen when an object suddenly changes position. Our conclusions are that the visual scene is first segmented into objects before a coherent velocity is assigned to the texture on each object''s surface. The omega effect arises because there are motion mechanisms that deal specifically with object rotation and these interact with pattern mechanisms sensitive to curvature.     

Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles

Domain formation is modeled on the surface of giant unilamellar vesicles using a Landau field theory model for phase coexistence coupled to elastic deformation mechanics (e.g., membrane curvature). Smooth particle applied mechanics, a form of smoothed particle continuum mechanics, is used to solve either the time-dependent Landau-Ginzburg or Cahn-Hilliard free-energy models for the composition dynamics. At the same time, the underlying elastic membrane is modeled using smooth particle applied mechanics, resulting in a unified computational scheme capable of treating the response of the composition fields to arbitrary deformations of the vesicle and vice versa. The results indicate that curvature coupling, along with the field theory model for composition free energy, gives domain formations that are correlated with surface defects on the vesicle. In the case that external deformations are included, the domain structures are seen to respond to such deformations. The present simulation capability provides a significant step forward toward the simulation of realistic cellular membrane processes.     

A sparse object coding scheme in area V4

Sparse coding has long been recognized as a primary goal of image transformation in the visual system. Sparse coding in early visual cortex is achieved by abstracting local oriented spatial frequencies and by excitatory/inhibitory surround modulation. Object responses are thought to be sparse at subsequent processing stages, but neural mechanisms for higher-level sparsification are not known. Here, convergent results from macaque area V4 neural recording and simulated V4 populations trained on natural object contours suggest that sparse coding is achieved in midlevel visual cortex by emphasizing representation of acute convex and concave curvature. We studied 165 V4 neurons with a random, adaptive stimulus strategy to minimize bias and explore an unlimited range of contour shapes. V4 responses were strongly weighted toward contours containing acute convex or concave curvature. In contrast, the tuning distribution in nonsparse simulated V4 populations was strongly weighted toward low curvature. But as sparseness constraints increased, the simulated tuning distribution shifted progressively toward more acute convex and concave curvature, matching the neural recording results. These findings indicate a sparse object coding scheme in midlevel visual cortex based on uncommon but diagnostic regions of acute contour curvature.     

Three-dimensional heart motion estimation using endoscopic monocular vision system: From artificial landmarks to texture analysis

In robot-assisted beating heart surgery, motion of the heart surface might be virtually stabilized to let the surgeon work as in on-pump cardiac surgery. Virtual stabilization means to compensate physically the relative motion between the instrument tool tip and the region of interest on the heart surface, and to offer surgeon a stable visual display of the scene. To this end, motion of the heart must be estimated. This article focusses on motion estimation of the heart surface. Two approaches are considered in the paper. The first one is based on landmark tracking allowing 3D pose estimation. The second is based on texture tracking. Classical computer vision methods, as well as a new texture-based tracking scheme has been applied to track the heart motion, and, when possible, reconstruct 3D distance to the heart surface. Experimental results obtained on in vivo images show the estimated motion of heart surface points.     

Quantification of phase synchronization phenomena and their importance for verbal memory processes

The tangential neurons in the lobula plate region of the flies are known to respond to visual motion across broad receptive fields in visual space.When intracellular recordings are made from tangential neurons while the intact animal is stimulated visually with moving natural imagery,we find that neural response depends upon speed of motion but is nearly invariant with respect to variations in natural scenery. We refer to this invariance as velocity constancy. It is remarkable because natural scenes, in spite of similarities in spatial structure, vary considerably in contrast, and contrast dependence is a feature of neurons in the early visual pathway as well as of most models for the elementary operations of visual motion detection. Thus, we expect that operations must be present in the processing pathway that reduce contrast dependence in order to approximate velocity constancy.We consider models for such operations, including spatial filtering, motion adaptation, saturating nonlinearities, and nonlinear spatial integration by the tangential neurons themselves, and evaluate their effects in simulations of a tangential neuron and precursor processing in response to animated natural imagery. We conclude that all such features reduce interscene variance in response, but that the model system does not approach velocity constancy as closely as the biological tangential cell.     

行带式柠条固沙林防风效果

传统观点研究认为：植被覆盖度低于40％,沙地处于半固定半流动状态．但在实践观察中发现：在低密度（或覆盖度）时,灌丛的水平分布格局对固定流沙和阻止风沙流的作用差异显著。以低覆盖度（20％-25％）的柠条固沙林为研究对象,采用多点式自记风速仪（GB-228）,在2。4月份的盛风季节,测定了行带式配置和随机分布的柠条固沙林以及完整的行带式配置和其中一带出现缺口的行带式固沙林内不同部位、不同高度的风速．统计分析风速测定结果发现：（1）当覆盖度在20％-25％时,行带式配置的柠条固沙林内的防风效果比同覆盖度随机分布的在20cm高处高48．4％;50era高处高30．7％;200cm高处高27．4％,且风速越大,行带式配置降低风速的效果越显著,当200cm高风速达到6—7m／s时,行带式的平均防风效果比同覆盖度随机分布的高48．2％;反映出在低覆盖度时,灌丛的水平分布格局成为制约固沙林沙防风效果的重要因素,行带式配置具有显著的防风效果;（2）在灌丛与灌丛之间形成的类似“狭管”流场的局部,有提升风速的作用,导致其林内观测的风速有约41．3％的观测结果超过旷野对照风速,行带式配置的柠条固沙林内没有一个观测结果超过对照风速;这个结果反映出随机分布的柠条固沙林内流场结构复杂、变化多样,也成为低覆盖度时,沙地处于半固定、半流动状态,疏林内同时存在风蚀和积沙和缺口处风速升高的重要因素;（3）行带式配置林内地表粗糙度比随机配置的高5．4-114．4倍,说明行带式配置具有显著的防止风蚀、固定流沙的作用;（4）行带式林内出现断带缺口处,其缺口处的风速降低有明显的累加现象;风速抬升现象在一定程度受到制约。这些结果为发展低覆盖度行带式配置的固沙林提供重要的科学依据。     

Iterative cooperation between parallel pathways for object and background motion

In a typical visual scene, one or more objects move relative to a larger background, which can itself be in motion as a result of the observer’s eyes moving with respect to the outside world. Here we show that accurate estimation of the background motion from an image velocity field can be accomplished through an iterative cooperation between two modules: one that specializes in calculating a weighted average velocity and another one calculating a velocity contrast map. We build on our analysis to provide a model for the tectum-pretectum loop in the nonmammalian midbrain. Our model accounts for some of the known properties of the tectal neurons (sensitivity to relative motion) and pretectal neurons (sensitivity to whole-field motion). It also agrees with our knowledge of the pretectotectal projection (divergent and inhibitory), and with the results of lesion studies in which the pretectal input to the tectum was removed, leading to hyperactivity of the tectal neurons and the animal. Our model also makes a testable prediction regarding the tectopretectal projection, i.e., that the presence of a larger object and a bigger discrepancy between the directions of motion for the object and the background lead to a larger error by the pretectum in estimating the background motion when the tectal input is abolished.     

Motion parallax contribution to perception of self-motion and depth

The object of this study is to mathematically specify important characteristics of visual flow during translation of the eye for the perception of depth and self-motion. We address various strategies by which the central nervous system may estimate self-motion and depth from motion parallax, using equations for the visual velocity field generated by translation of the eye through space. Our results focus on information provided by the movement and deformation of three-dimensional objects and on local flow behavior around a fixated point. All of these issues are addressed mathematically in terms of definite equations for the optic flow. This formal characterization of the visual information presented to the observer is then considered in parallel with other sensory cues to self-motion in order to see how these contribute to the effective use of visual motion parallax, and how parallactic flow can, conversely, contribute to the sense of self-motion. This article will focus on a central case, for understanding of motion parallax in spacious real-world environments, of monocular visual cues observable during pure horizontal translation of the eye through a stationary environment. We suggest that the global optokinetic stimulus associated with visual motion parallax must converge in significant fashion with vestibular and proprioceptive pathways that carry signals related to self-motion. Suggestions of experiments to test some of the predictions of this study are made.     

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.