Bert Willems

Multiple Routes to Object Matching from Different Viewpoints: Mental Rotation versus Invariant Features

Previous research has shown that object recognition from different viewpoints often yields strong effects of viewpoint. However, for some objects and experimental paradigms almost complete viewpoint invariance is obtained. This suggests the existence of multiple routes to object recognition. In this study we further strengthen this notion by designing two different conditions using the same experimental paradigm (simultaneous matching) and highly similar objects (multiblock figures). In the first condition (involving a handedness violation), strong effects of viewpoint were obtained. In the second condition (involving an invariance violation), the effects of viewpoint were negligible. This result illustrates that asking under what circumstances object recognition is viewpoint dependent or independent is more fruitful than attempting to show that object recognition is either viewpoint dependent or independent.

Cournot Equilibrium in Price-Capped Two-Settlement Electricity Markets

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time and competitive entry opportunities, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above a certain level. Another more direct approach is to cap spot prices through regulatory intervention. In this paper we explore the implications of the two alternative mechanisms in a two settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and market power. As an illustrative test case we use the 53-bus Belgian electricity network with representative generator cost but hypothetical demand and ownership assumptions. When compared to two-settlement systems without price caps we find that either of the price capping alternatives results in reduced forward contracting. Furthermore the reduction in spot prices due to forward contracting is smaller.

Matching multicomponent objects from different viewpoints : Mental rotation as normalization?

Novel multicomponent objects were created, and 3 distractors were created for each object by changing the relations between the parts of the object. In a set of 5 experiments, target objects were presented as a motion sequence of multiple views or as a single view. Participants were asked to determine whether an image of an object, viewed from another viewpoint, was the same as the target object. The axis of rotation was aligned with one of the environmental axes or with the main axis of the object. The effects of viewpoint on performance imply that the matching of objects is viewpoint dependent and requires a process of normalization to undo the differences between the perceptual description and the stored object descriptions. The lack of a systematic effect of the axis of rotation, however, suggests that this normalization is best understood as not involving a 3-D transformation of stored 3-D object models.

The viewpoint-dependency of veridicality: Psychophysics and modelling

Human observers were shown projected angles, embedded in solid cross-like figures and were asked whether these projected angles could be the projection of an orthogonal angle in 3-D space (i.e. whether the two legs of the cross were orthogonal to each other). We found that performance depended on the viewpoint at which the angle was viewed: Both slant (i.e. the angle between the normal of the target angle relative to the plane of projection) and roll (i.e. the rotation around the normal of the target angle) had a systematic effect on the proportion of errors when observers were shown non-orthogonal angles. With orthogonal angles, however, this effect was absent (i.e. very low error rate with no systematic effect of slant and roll). Instead of assuming a viewpoint-dependent bias towards orthogonality, a computational analysis of the task, using a Bayesian approach, and a computer simulation showed that the viewpoint-dependency can be modelled by a fixed set of biases in order to constrain the set of possible scenes that could give rise to the projection.

The influence of two-dimensional stimulus properties in a reconstruction task with minimal information stimuli

Effects of viewpoint that are typically found in shape recognition tasks have been interpreted in the past as strong evidence against approaches based on the use of geometric invariants by the human visual system. At first sight, the use of such invariants would indeed predict shape recognition to be viewpoint independent. It has been argued before, however, that the visual estimation of invariants need not itself be invariant. Changes of viewpoint introduce changes in 2D stimulus features. The latter may make the estimation of invariants by the visual system more or less difficult. The present study explores how such 2D features influence estimation distributions in a reconstruction paradigm. Subjects were shown four coplanar dots. They were asked to estimate the position of one of the dots relative to the three others on the basis of a slanted version of the configuration. An estimation distribution was obtained for every position of the dot to be estimated. Biases in these distributions indicated that subjects performed the task by using 2D reference axes that were unambiguously identifiable in both the images of the dot pattern.