Temporal integration in structure from motion

n/

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

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

Perceived slant from optic flow in active and passive viewing of natural and virtual surfaces

Motivation. Recent evidence suggests that extra-retinal signals play an important role in the perception of 3D structure from motion (SfM). According to the stationarity assumption (SA, Wexler, Lamouret, & Droulez, 2001), a correct solution to the SfM problem can be found for a moving observer viewing a stationary object, by assuming a veridical estimate of the observer's translation. According to SA, perception of surface slant should be: (1) more accurate for active than for passive vision; (2) more accurate for natural than for virtual objects (because of the cue-conflict inherent to virtual stimuli). Method. We performed three experiments involving both active and passive observers. The task was to estimate the slant of a static random-dot planar surface. We manipulated the surface slant and the translation speed the observer's head. The translational displacements and orientation of the participant's head were recorded on-time by an Optotrack Certus system and the virtual stimuli were generated in real time on a high-definition CRT (passive observers received a replay of the same optic flow). Natural simuli were dotted planar surfaces. Results. Perceived surface orientation increased with both increasing slant and translation velocity. These systematic biases were found for both virtual and natural stimuli, and for both active and passive observers. Conclusion. Extra-retinal information available to active vision is not sufficient for a veridical solution to the SfM problem. Also for active vision, the first-order properties of the optic flow are the main determinant of perceived surface slant. If the first-order properties of the optic flow are kept constant, the surface is perceived as having a constant orientation, regardless of actual orientation; if the first-order properties of the optic flow are varied (e.g., by manipulating the translation speed of the observer's head), surface slant is perceived as varying, regardless of whether distal slant is constant