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P Werkhoven

Publications and source records attributed to P Werkhoven.

15 recordsLinked to original sources

Metamerisms in Structure-from-motion perception.

As a three-dimensional object is moving through our world, we generally obtain a vivid impression of both its structure and its motion through space. The time-course of two-dimensional projections of the scene (optic flow) is important in conveying this three-dimensional information to us. The extent to which we can solve this specific inverse problem, i.e. infer a three-dimensional scene from two-dimensional flow, depends on the accuracy with which the required flow characteristics are processed by our visual system. In adequate two-dimensional processing can lead to incomplete representations of the three-dimensional world (three-dimensional metric information is lost). Then the motion and structure of objects can no longer be recovered uniquely. Consequently, metameric classes of three-dimensional representations arise (e.g. only affine properties are conserved). this study investigates under what conditions we find metameric combinations of the perceived attitude and perceived rotation of a plane. Our subjects are presented with stimuli consisting of two horizontally separated planar patches rotating back and forth in depth about vertical axes. Subjects are required to match both the attitude and the rotation magnitude of these two patches. We vary the attitude from 15 to 60 deg vertical slant, and the rotation magnitude from 28 to 98 deg. We find that the matched slant and rotation settings vary widely. For high slant values and for small rotations, attitude and rotation settings become highly correlated, suggesting metamery. For low slant values and for large rotations, the correlation almost disappears, suggesting that both quantities are estimated independently and uniquely. Our paradigm reveals that with one task and one type of stimulus a gradual transition occurs from unique settings (metric representations) to metameric classes of settings (e.g. affine representations).

Depth Perception

Discriminating the volume of motion-defined solids.

We investigated the ability of human observers to discriminate an important global 3-D structural property, namely volume, of motion-defined objects. We used convex transparent wire-frame objects consisting of about 12 planar triangular facets. Two objects, vertically separated by 7 degrees, were shown simultaneously on a computer display. Both revolved at 67 degrees/sec around a common vertical axis through their centers of mass. Observers watched the objects monocularly for an average of three full rotations before they responded. We measured volume discrimination as a function of absolute volume (3-48 cm3; 1 m viewing distance) and shape (cubes, rods, and slabs of different regularity). We found that (1) volume discrimination performance can be described by Weber's law, (2) Weber fractions depend strongly on the particular combination of shapes used (regular shapes, especially cubes, are easiest to compare, and similar shapes are easier to compare than different shapes), and (3) humans use a representation of volume that is more veridical and stable in the sense of repeatability than a strategy based on the average visible (2-D) area would yield.

Depth Perception

Cross-modal slant and curvature matching of stereo- and motion-induced surfaces.

In many laboratory setups and in many day-to-day situations, a unique solution of the structure-from-two-views problem is unobtainable. Yet, when the visual system is presented with two projections in a sequence, it nevertheless appears to generate a reasonably stable percept of structure. In the research reported here, we examined whether the same surface would be perceived when subjects were presented with a pair of views that alternated in time monocularly (two-frame motion) or were shown simultaneously to both eyes (stereo). In Experiment 1, we studied slant perception: human observers were asked to match the slant of a motion-induced planar surface with its stereo-induced counterpart. In Experiment 2, the perceived curvature of parabolic surfaces was matched in a similar way. The results show that motion-induced slant is matched with a higher value of the stereo-induced slant. However, the curvature experiment showed that motion-induced curvature is matched with a lower stereo-induced curvature. One possible explanation may be that the slant and curvature are internally inconsistent in at least one of the modalities.

Attention

Extraction of relief from visual motion.

We quantified the ability of human subjects to discriminate the relative distance of two points from a slanted plane when viewing the projected velocities of this scene (orthographic projection). The relative distance from a plane (called relief) is a 3-D property that is invariant under linear (affine) transformations. As such, relief can in principle be extracted from the instantaneous projected velocity field; a metric representation, which requires the extraction of visual acceleration, is not required. The stimulus consisted of a slanted plane P (specified by three points) and two points Q1 and Q2 that are non-coplanar with P. This configuration of points oscillated rigidly around the vertical axis. We have measured the systematic error and accuracy with which human subjects estimate the relative distance of points Q1 and Q2 from plane P as a function of the slant of P. The systematic error varies with slant: it is low for small slant values, reaches a maximum for medium slant values, and drops again for high slant values. The accuracy covaries with the systematic error and is thus high for small and large slant values and low for medium slant values. These results are successfully modeled by a simple relief-from-motion computation based on local estimates of projected velocities. The data are well predicted by assuming (1) a measurement error in velocity estimation that varies proportionally to velocity (Weber's law) and (2) an eccentricity-dependent underestimation of velocity.

Acceleration

Non-Fourier motion analysis.

It has been realized for some time that the visual system performs at least two general sorts of motion processing. First-order motion processing applies some variant of standard motion analysis (i.e. spatiotemporal Fourier energy analysis) directly to stimulus luminance, whereas second-order motion processing applies standard motion analysis to one or another grossly non-linear transformation of stimulus luminance. We have developed a method for disentangling the different sorts of mechanisms that may operate in human vision to detect second-order motion. This method hinges on an empirical condition called transition invariance that may or may not be satisfied by a family psi of textures. Any failure of this condition indicates that more than one mechanism is involved in detecting the motion of stimuli composed of the textures in psi. We have shown that the family of sinusoidal gratings oriented orthogonally to the direction of motion and varying in contrast and spatial frequency is transition invariant. We modelled the results in terms of a single-channel motion computation. We have new results indicating that a specific class of textures differing in texture element density and texture element contrast decisively fails the test of transition invariance. These findings suggest that in addition to the single second-order motion channel required by our earlier results there exists at least one other second-order motion channel. We argue that the preprocessing transformation used by this channel is a pointwise non-linearity that maps stimulus contrasts of absolute value less than some relatively high threshold tau onto 0, but increases with magnitude of c-tau for contrasts. c of absolute value greater than tau.

Animals

Perception of apparent motion between dissimilar gratings: spatiotemporal properties.

What determines the strength of texture-defined apparent motion perception when the stimulus has no net directional energy in the Fourier domain? In a previous paper [Werkhoven, Sperling & Chubb (1993) Vision Research, 33, 463-485] we demonstrated the counterintuitive finding that the correspondence in spatial frequency and in modulation amplitude between neighboring patches of texture in a spatiotemporal motion path are irrelevant to motion strength. Instead, we found strong support for what we call a single channel or one-dimensional motion computation: a simple nonlinear transformation of the image, followed by standard motion analysis. Here, we further studied the dimensionality of the motion computation in a parameter space that includes texture orientation and stimulus display rate in addition to texture spatial frequency and modulation amplitude. We used ambiguous motion displays in which one motion path, consisting of patches of nonsimilar texture, competes with another motion path comprised entirely of similar texture patches. The data show that motion between dissimilar patches of texture that are orthogonally oriented, have a two octave difference in spatial frequency and differ 50% in modulation amplitude can easily dominate motion between similar patches of texture. A single channel accounts for more than 70% of texture-from-motion strength for the parameter space examined and this channel is invariant for stimulus display rates varying over a four-fold range.

Humans

The dimensionality of texture-defined motion: a single channel theory.

We examine apparent motion carried by textural properties. The texture stimuli consist of a sequence of grating patches of various spatial frequencies and amplitudes. Phases are randomized between frames to insure that first-order motion mechanisms directly applied to stimulus luminance are not systematically engaged. We use ambiguous apparent motion displays in which a heterogeneous motion path defined by alternating patches of texture s (standard) and texture v (variable) competes with a homogeneous motion path defined solely by patches of texture s. Our results support a one-dimensional (single-channel) model of motion-from-texture in which motion strength is computed from a single spatial transformation of the stimulus--an activity transformation. The value assigned to a point in space-time by this activity transformation is directly proportional to the modulation amplitude of the local texture and inversely proportional to local spatial frequency (within the range of spatial frequencies examined). The activity transformation is modeled as the rectified output of a low-pass spatial filter applied to stimulus contrast. Our data further suggest that the strength of texture-defined motion between a patch of texture s and a patch of texture v is proportional to the product of the activities of s and v. A strongly counterintuitive prediction of this model borne out in our data is that motion between patches of different texture can be stronger than motion between patches of similar texture (e.g. motion between patches of a low contrast, low frequency texture 1 and patches of high contrast, high frequency texture h can be stronger than motion between patches of similar texture h).

Contrast Sensitivity

Visual size invariance does not apply to geometric angle and speed of rotation.

The ability of humans to visually estimate geometric angle and speed of rotation was examined as a function of the spatial scale of the stimuli. Both properties are objectively invariant at different spatial scales, but the results of experiments show that the judgement of acute geometric angles as well as that of speed of rotation varies strongly and monotonically with the scale of presentation. If the image is magnified, the perceived geometric angle and the perceived speed of rotation increase. If the image is reduced in size, they decrease. This result imposes strong constraints on perceptual theories.

Adult

Visual processing of optic acceleration.

We present data on the human sensitivity to optic acceleration, i.e. temporal modulations of the speed and direction of moving objects. Modulation thresholds are measured as a function of modulation frequency and speed for different periodical velocity vector modulation functions using a localized target. Evidence is presented that human detection of velocity vector modulations is not directly based on the acceleration signal (the temporal derivative of the velocity vector modulation). Instead, modulation detection is accurately described by a two-stage model: a low-pass temporal filter transformation of the true velocity vector modulation followed by a variance detection stage. A functional description of the first stage is a second order low-pass temporal filter having a characteristic time constant of 40 msec. In effect, the temporal low-pass filter is an integration of the velocity vector modulation within a temporal window of 100-140 msec. A non-trivial link of this low-pass filter stage to the temporal characteristics of standard motion detection mechanisms will be discussed. Velocity vector modulations are detected in the second-stage, whenever the variance of the filtered velocity vector exceeds a certain threshold variance in either the speed or direction dimension. The threshold standard deviations for this variance detection stage are estimated to be 17% for speed modulations and 9% for motion direction modulations.

Fixation, Ocular

Reversed rotary motion perception.

A stroboscopically presented revolving annulus composed of dots is used to elicit rotary motion perception. Observers judge the direction of rotary motion. We find sharp and gradual transitions in the probability for reversed motion perception as a function of the angle of rotation between successive frames. These transitions reveal that matches between nonsuccessive frames can dominate motion perception. The transitions are scale invariant. The strength of a match is discussed in terms of a motion strength function, which is a separable function of the angle of rotation between successive frames and the frame repetition rate. The dependence of motion strength on the frame repetition rate (time function) is computed from the transitions. The similarity of this time function for rotary motion with the time function for linear motion [Psychol. Rev. 88, 171 (1981)] suggests that mechanisms for the discrimination of rotary motion address local detectors of linear motion.

Humans

Visual processing of rotary motion.

Local descriptions of velocity fields (e.g., rotation, divergence, and deformation) contain a wealth of information for form perception and ego motion. In spite of this, human psychophysical performance in estimating these entities has not yet been thoroughly examined. In this paper, we report on the visual discrimination of rotary motion. A sequence of image frames is used to elicit an apparent rotation of an annulus, composed of dots in the frontoparallel plane, around a fixation spot at the center of the annulus. Differential angular velocity thresholds are measured as a function of the angular velocity, the diameter of the annulus, the number of dots, the display time per frame, and the number of frames. The results show a U-shaped dependence of angular velocity discrimination on spatial scale, with minimal Weber fractions of 7%. Experiments with a scatter in the distance of the individual dots to the center of rotation demonstrate that angular velocity cannot be assessed directly; perceived angular velocity depends strongly on the distance of the dots relative to the center of rotation. We suggest that the estimation of rotary motion is mediated by local estimations of linear velocity.

Adult

Extraction of motion parallax structure in the visual system. I.

We present a paradigm to estimate local affine motion parallax structure from a varying image irradiance pattern. The method is based on a matching of jets of irradiance rather than the local image irradiance pattern or features of it. It does not put any constraints on the structure of the image irradiance pattern. Moreover, the aperture problem does not arise and additional ad hoc constraints on the velocity field like the "smoothness constraint" are superfluous. An implementation is designed such that the affine structure of the local motion parallax field is represented through simple combinations of the outputs of physiologically plausible receptive fields and their temporal derivatives.

Cybernetics

Extraction of motion parallax structure in the visual system. II.

We have developed an algorithm to extract local affine motion parallax structure of a varying image irradiance pattern in Part I. In Part II, we present computational results of this algorithm for situations in which the information about the affine structure is contained in only two successive images. This applies to a large class of problems (e.g. two-image motion sequences and stereoscopic vision). The results show the effects of spatio-temporal discretisation and internal noise on the performance of this algorithm.

Algorithms

Effects of element orientation on apparent motion perception.

We present an ambiguous motion paradigm that allows us to quantify the influence of aspects of form relevant to the perception of apparent motion. We report on the role of bar element orientation in motion paths. The effect of orientation differences between bar elements in a motion path is small with respect to the crucial role of the orientation of bar elements relative to motion direction. Motion perception between elements oriented along the motion direction dominates motion perception between elements oriented perpendicularly to motion direction. The perception of apparent motion is affected by bar length and width and is anisotropic.

Attention

Pulse modulation detection in human motion vision.

We present data on the human sensitivity to temporal pulse modulations of target velocity. We measured threshold detection modulation amplitudes for pulse-shaped speed modulations, as a function of pulse duration and temporal frequency. At short pulse durations (up to 50 msec) and low modulation frequency (1 Hz), detection amplitudes are ruled by Bloch's law: the product of pulse duration and threshold modulation amplitude is a constant. This constant corresponds to a position modulation with an amplitude of 3 arc min in a coordinate frame that moves at the average speed (3 deg/sec) of the target. At longer pulse durations we find deviations from Bloch's law. Speed modulation thresholds are not critically dependent on target luminance contrast. These results are modeled by a modulation detection process in two stages. A functional description of the first stage is filtering of the true speed modulation signal by a second order low-pass filter with a characteristic time constant of 20-25 msec. The second (decision) stage is variance detection: modulations are detected when the variance of the filtered modulation function exceeds a certain threshold variance. The square-root threshold variance is estimated 8-10%. This two-parameter model accurately predicts the measured dependence of pulse modulation detection thresholds on pulse duration and pulse density.

Filtration