Perceived surface slant is systematically biased in the actively-generated optic flow

Humans make systematic errors in the 3D interpretation of the optic flow in both passive and active vision. These systematic distortions can be predicted by a biologically-inspired model which disregards self-motion information resulting from head movements (Caudek, Fantoni, & Domini 2011). Here, we tested two predictions of this model: (1) A plane that is stationary in an earth-fixed reference frame will be perceived as changing its slant if the movement of the observer's head causes a variation of the optic flow; (2) a surface that rotates in an earth-fixed reference frame will be perceived to be stationary, if the surface rotation is appropriately yoked to the head movement so as to generate a variation of the surface slant but not of the optic flow. Both predictions were corroborated by two experiments in which observers judged the perceived slant of a random-dot planar surface during egomotion. We found qualitatively similar biases for monocular and binocular viewing of the simulated surfaces, although, in principle, the simultaneous presence of disparity and motion cues allows for a veridical recovery of surface slant.     

Bayesian modeling of perceived surface slant from actively-generated and passively-observed optic flow

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physical or virtual surfaces. These distortions are modulated by head translation speed, with perceived slant increasing directly with the local velocity gradient of the optic flow. This empirical result allows us to determine the relative merits of two alternative approaches aimed at explaining perceived surface slant in active vision: an "inverse optics" model that takes head motion information into account, and a probabilistic model that ignores extra-retinal signals. We compare these two approaches within the framework of the bayesian theory. The "inverse optics" bayesian model produces veridical slant estimates if the optic flow and the head translation velocity are measured with no error; because of the influence of a "prior" for flatness, the slant estimates become systematically biased as the measurement errors increase. The bayesian model, which ignores the observer's motion, always produces distorted estimates of surface slant. Interestingly, the predictions of this second model, not those of the first one, are consistent with our empirical findings. The present results suggest that (a) in active vision perceived surface slant may be the product of probabilistic processes which do not guarantee the correct solution, and (b) extra-retinal signals may be mainly used for a better measurement of retinal information.     

Computing the direction of heading from affine image flow

Observers moving through a three-dimensional environment can use optic flow to determine their direction of heading. Existing heading algorithms use cartesian flow fields in which image flow is the displacement of image features over time. I explore a heading algorithm that uses affine flow instead. The affine flow at an image feature is its displacement modulo an affine transformation defined by its neighborhood. Modeling the observer's instantaneous motion by a translation and a rotation about an axis through its eye, affine flow is tangent to the translational field lines on the observer's viewing sphere. These field lines form a radial flow field whose center is the direction of heading. The affine flow heading algorithm has characteristics that can be used to determine whether the human visual system relies on it. The algorithm is immune to observer rotation and arbitrary affine transformations of its input images; its accuracy improves with increasing variation in environmental depth; and it cannot recover heading in an environment consisting of a single plane because affine flow vanishes in this case. Translational field lines can also be approximated through differential cartesian motion. I compare the performance of heading algorithms based on affine flow, differential cartesian flow, and least-squares search.     

Be careful with your principal components

Principal components analysis (PCA) is a common method to summarize a larger set of correlated variables into a smaller and more easily interpretable axes of variation. However, the different components need to be distinct from each other to be interpretable otherwise they only represent random directions. This is a fundamental assumption of PCA and, thus, needs to be tested every time. Sample correlation matrices will always result in a pattern of decreasing eigenvalues even if there is no structure. Tests are, therefore, needed to discern real patterns from illusionary ones. Furthermore, the loadings of the vectors need to be larger than expected by random data to be useful in the calculation of PC‐scores. PC‐scores calculated from nondistinct PC's have very large standard errors and cannot be used for biological interpretations. I give a number of examples to illustrate the potential problems with PCA. Robustness of the PC's increases with increasing sample size but not with the number of traits. I review a few simple test statistics appropriate for testing PC's and use a real‐world example to illustrate how this can be done using randomization tests. PCA can be very useful but great care is needed to avoid spurious results.     

Insect-Inspired Self-Motion Estimation with Dense Flow Fields—An Adaptive Matched Filter Approach

The control of self-motion is a basic, but complex task for both technical and biological systems. Various algorithms have been proposed that allow the estimation of self-motion from the optic flow on the eyes. We show that two apparently very different approaches to solve this task, one technically and one biologically inspired, can be transformed into each other under certain conditions. One estimator of self-motion is based on a matched filter approach; it has been developed to describe the function of motion sensitive cells in the fly brain. The other estimator, the Koenderink and van Doorn (KvD) algorithm, was derived analytically with a technical background. If the distances to the objects in the environment can be assumed to be known, the two estimators are linear and equivalent, but are expressed in different mathematical forms. However, for most situations it is unrealistic to assume that the distances are known. Therefore, the depth structure of the environment needs to be determined in parallel to the self-motion parameters and leads to a non-linear problem. It is shown that the standard least mean square approach that is used by the KvD algorithm leads to a biased estimator. We derive a modification of this algorithm in order to remove the bias and demonstrate its improved performance by means of numerical simulations. For self-motion estimation it is beneficial to have a spherical visual field, similar to many flying insects. We show that in this case the representation of the depth structure of the environment derived from the optic flow can be simplified. Based on this result, we develop an adaptive matched filter approach for systems with a nearly spherical visual field. Then only eight parameters about the environment have to be memorized and updated during self-motion.     

The computation of structure from fixed-axis motion: rigid structures

We show that three distinct orthographic views of three points in a rigid configuration are compatibel with at most 64 interpretations of the three-dimensional structure and motion of the points. If, in addition, one assumes that the three points spin about a fixed axis over the three views, then with probability one there is a unique three-dimensional interpretation (plus a reflection). Moreover the probability of false targets is zero. In the special case that the axis of rotation is parallel to the image plane three views of the three points are sufficient to obtain at most two interpretations (plus reflections)-unless one assumes the angular velocity about the axis is constant, in which case three views of two points are sufficient to determine a unique interpretation. Closed form solutions are obtained for each of these cases. The systems of equations studied here are in each case overconstraining (i.e. there are more independent equations than unknowns) and are amenable to solution by nonlinear programming. These two properties make possible the construction of noise insensitive algorithms for computer vision systems. Our uniqueness proofs employ the Principle of upper semicontinuity, a principle which underlies a general mathematical framework for the analysis of solutions to overconstraining systems of equations.     

Honeybees' speed depends on dorsal as well as lateral, ventral and frontal optic flows

Flying insects use the optic flow to navigate safely in unfamiliar environments, especially by adjusting their speed and their clearance from surrounding objects. It has not yet been established, however, which specific parts of the optical flow field insects use to control their speed. With a view to answering this question, freely flying honeybees were trained to fly along a specially designed tunnel including two successive tapering parts: the first part was tapered in the vertical plane and the second one, in the horizontal plane. The honeybees were found to adjust their speed on the basis of the optic flow they perceived not only in the lateral and ventral parts of their visual field, but also in the dorsal part. More specifically, the honeybees' speed varied monotonically, depending on the minimum cross-section of the tunnel, regardless of whether the narrowing occurred in the horizontal or vertical plane. The honeybees' speed decreased or increased whenever the minimum cross-section decreased or increased. In other words, the larger sum of the two opposite optic flows in the horizontal and vertical planes was kept practically constant thanks to the speed control performed by the honeybees upon encountering a narrowing of the tunnel. The previously described ALIS ("AutopiLot using an Insect-based vision System") model nicely matches the present behavioral findings. The ALIS model is based on a feedback control scheme that explains how honeybees may keep their speed proportional to the minimum local cross-section of a tunnel, based solely on optic flow processing, without any need for speedometers or rangefinders. The present behavioral findings suggest how flying insects may succeed in adjusting their speed in their complex foraging environments, while at the same time adjusting their distance not only from lateral and ventral objects but also from those located in their dorsal visual field.     

Distinguishing heat from light in debate over controversial fossils

Fossil organisms offer our only direct insight into how the distinctive body plans of extant organisms were assembled. However, realizing the potential evolutionary significance of fossils can be hampered by controversy over their interpretation. Here, as a guide to evaluating palaeontological debates, we outline the process and pitfalls of fossil interpretation. The physical remains of controversial fossils should be reconstructed before interpreting homologies, and choice of interpretative model should be explicit and justified. Extinct taxa lack characters diagnostic of extant clades because the characters had not yet evolved, because of secondary loss, or because they have rotted away. The latter, if not taken into account, will lead to the spurious assignment of fossils to basally branching clades. Conflicting interpretations of fossils can often be resolved by considering all the steps in the process of anatomical analysis and phylogenetic placement, although we must accept that some fossil organisms are simply too incompletely preserved for their evolutionary significance to be realized.     

Two-dimensional coding of linear acceleration and the angular velocity sensitivity of the otolith system

There exist otolith-sensitive vestibular nuclei neurons with spatio-temporal properties that can be described by two response vectors that are in temporal and spatial quadrature. These neurons respond to the component of a stimulus vector on a plane rather than a single axis. It is demonstrated here that these two-dimensional linear accelerometer neurons can function as one-dimensional angular velocity detectors. The two-dimensional property in both space and time allows these neurons to encode the component of the stimulus angular velocity vector that is normal to the plane defined by the two response vectors. The angular velocity vector in space can then be reconstructed by three populations of such neurons having linearly independent response planes. Thus, we propose that these two-dimensional spatio-temporal linear accelerometer neurons, in addition to participating in functions of the otolith system that are based on detection of linear acceleration, are also involved in the generation of compensatory ocular responses during off-vertical axis rotations.     

Novel method to correct displacement profile images and calculate flow vector fields using saturation-tagging MR imaging.

Saturation-tagging Magnetic Resonance (MR) imaging provides a simple and robust means to directly visualize displacement profiles within fluid flow fields. Although useful for velocity quantitation as well as for qualitative depiction of flow patterns in certain well-defined flow fields, the technique is prone to distortions due to oblique flow (misregistration artifact) and ambiguity of fluid vector trajectories in complex flow situations. A novel method is proposed whereby two images are acquired, differing in the temporal position of the phase encoding gradient. Theoretical analysis shows that from the paired images, distortion of the two-dimensional displacement profile can be corrected and fluid velocity vectors extracted, even if the flow directions are unknown. In the simpler case of flow oblique to the gradient principal axes, but with a known trajectory, only one image is necessary to correct the displacement profile distortion and extract the velocity information. MRI experiments in a straight tube model have been carried out to evaluate the feasibility of this method. Good agreement is achieved between the results from MR imaging and those predicted via computer simulation.     

Microscopic velocimetry with a scaled-up model for evaluating a flow field over cultured endothelial cells

A microscopic velocimetry technique for evaluating the flow field over cultured endothelial cells was developed. Flow around a cell model scaled up by a factor of 100 was visualized by using an optical microscope and was quantified by using particle-tracking velocimetry. Wall shear stress on the model surface was determined from a two-dimensional velocity field interpolated from measured velocity vectors. Accuracy of the velocimetry was verified by measuring the flow over a sinusoidal cell model that had a wall shear stress profile analytically determined with linear perturbation theory. Comparison of the experimental results with the analytical solution revealed that the total error of the measured wall shear stress was 6 percent.     

Kelvin-Helmholtz instability in a bounded plasma flow

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfvén velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth’s magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfvén velocity.     

Optic flow estimation on trajectories generated by bio-inspired closed-loop flight

We generated panoramic imagery by simulating a fly-like robot carrying an imaging sensor, moving in free flight through a virtual arena bounded by walls, and containing obstructions. Flight was conducted under closed-loop control by a bio-inspired algorithm for visual guidance with feedback signals corresponding to the true optic flow that would be induced on an imager (computed by known kinematics and position of the robot relative to the environment). The robot had dynamics representative of a housefly-sized organism, although simplified to two-degree-of-freedom flight to generate uniaxial (azimuthal) optic flow on the retina in the plane of travel. Surfaces in the environment contained images of natural and man-made scenes that were captured by the moving sensor. Two bio-inspired motion detection algorithms and two computational optic flow estimation algorithms were applied to sequences of image data, and their performance as optic flow estimators was evaluated by estimating the mutual information between outputs and true optic flow in an equatorial section of the visual field. Mutual information for individual estimators at particular locations within the visual field was surprisingly low (less than 1 bit in all cases) and considerably poorer for the bio-inspired algorithms that the man-made computational algorithms. However, mutual information between weighted sums of these signals and comparable sums of the true optic flow showed significant increases for the bio-inspired algorithms, whereas such improvement did not occur for the computational algorithms. Such summation is representative of the spatial integration performed by wide-field motion-sensitive neurons in the third optic ganglia of flies.     

Birefringent Objects Visualized by Circular Polarization Microscopy

In the standard polarizing microscope, birefringent material appears bright only if its optic axis is oblique to the axes of the polarizer and analyzer filters; consequently, an object may be visualized as several disconnected bright regions. This confusing appearance is avoided if the crossed plane polarizers of the conventional microscope are replaced by circular polarizers of opposite handedness. All orientations of the optic axis in the foal plane then become equivalent; objects generally appear uniformly bright. Ordinary microscopes are easily modified to use this technic with readily available components.     

Birefringent objects visualized by circular polarization microscopy

In the standard polarizing microscope, birefringent material appears bright only if its optic axis is oblique to the axes of the polarizer and analyzer filters; consequently, an object may be visualized as several disconnected bright regions. This confusing appearance is avoided if the crossed plane polarizers of the conventional microscope are replaced by circular polarizers of opposite handedness. All orientations of the optic axis in the focal plane then become equivalent; objects generally appear uniformly bright. Ordinary microscopes are easily modified to use this technic with readily available components.     

The flow field downstream of an oscillating collapsed tube

A two-component laser Doppler anemometer was used to determine the velocity of aqueous flow in the region from 0.25 to 2.5 diameters downstream of a collapsible tube while the tube was executing vigorous repetitive flow-induced oscillations. The Reynolds number for the time-averaged flow was 10,750. A simultaneous measurement of the pressure at the downstream end of the tube was used to align all the results in time at sixty locations in each of the two principal planes defined by the axes of collapse of the flexible tube upstream. The raw data of seed-particle velocity were used to create a periodic waveform for each measured velocity component at each location by least-squares fitting of a Fourier series. The results are presented as both velocity vectors and interpolated contours, for each of ten salient instants during the cycle of oscillation. In the plane of the collapse major axis, the dominant feature is the jet which emerges from each of the two tube lobes when it collapses, but transient retrograde flow is observed on both the central and lateral edges of this jet. In the orthogonal, minor-axis plane, the dominant feature is the retrograde flow, which during part of the cycle extends over the whole plane. All these features are essentially confined to the first 1.5 diameters of the rigid pipe downstream of the flexible tube. These data map the temporal and spatial extent of the highly three-dimensional reversing flow just downstream of an oscillating collapsed tube.     

Modeling the influence of optic flow on grid cell firing in the absence of other cues1

Information from the vestibular, sensorimotor, or visual systems can affect the firing of grid cells recorded in entorhinal cortex of rats. Optic flow provides information about the rat’s linear and rotational velocity and, thus, could influence the firing pattern of grid cells. To investigate this possible link, we model parts of the rat’s visual system and analyze their capability in estimating linear and rotational velocity. In our model a rat is simulated to move along trajectories recorded from rat’s foraging on a circular ground platform. Thus, we preserve the intrinsic statistics of real rats’ movements. Visual image motion is analytically computed for a spherical camera model and superimposed with noise in order to model the optic flow that would be available to the rat. This optic flow is fed into a template model to estimate the rat’s linear and rotational velocities, which in turn are fed into an oscillatory interference model of grid cell firing. Grid scores are reported while altering the flow noise, tilt angle of the optical axis with respect to the ground, the number of flow templates, and the frequency used in the oscillatory interference model. Activity patterns are compatible with those of grid cells, suggesting that optic flow can contribute to their firing.     

The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip

In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.     

New robust face recognition methods based on linear regression

Nearest subspace (NS) classification based on linear regression technique is a very straightforward and efficient method for face recognition. A recently developed NS method, namely the linear regression-based classification (LRC), uses downsampled face images as features to perform face recognition. The basic assumption behind this kind method is that samples from a certain class lie on their own class-specific subspace. Since there are only few training samples for each individual class, which will cause the small sample size (SSS) problem, this problem gives rise to misclassification of previous NS methods. In this paper, we propose two novel LRC methods using the idea that every class-specific subspace has its unique basis vectors. Thus, we consider that each class-specific subspace is spanned by two kinds of basis vectors which are the common basis vectors shared by many classes and the class-specific basis vectors owned by one class only. Based on this concept, two classification methods, namely robust LRC 1 and 2 (RLRC 1 and 2), are given to achieve more robust face recognition. Unlike some previous methods which need to extract class-specific basis vectors, the proposed methods are developed merely based on the existence of the class-specific basis vectors but without actually calculating them. Experiments on three well known face databases demonstrate very good performance of the new methods compared with other state-of-the-art methods.     

Measurement of propulsive power and evaluation of propulsive performance from the wake of a self-propelled vehicle

Propulsive efficiency is a key indicator of propulsive performance, but it can be difficult to measure when the propulsion system is integrated into the vehicle body because the average rate of useful work done propelling the vehicle (Wu) and/or the average mechanical power expended propelling the vehicle (Pmech) is not known directly. A general approach would be to determine either or both of (Wu) and (Pmech) from the vehicle wake. The present discussion demonstrates that only (Pmech) can be determined from the flow crossing a plane a fixed (average) distance downstream of the vehicle. A method for measuring (Pmech) is presented using the observation that the power required to tow a permeable obstruction behind the vehicle depends on (Pmech). Several methods for evaluating propulsive performance using [Formula: see text] are proposed, including the definition of an equivalent jet velocity and corresponding Froude efficiency if the time-averaged mass flow rate through the propulsion system is known. If only (Pmech) is known, the recommended measure of propulsive performance is a power coefficient defined analogous to a drag coefficient.