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If one nondescript object’s volume is twice that of another, is it necessarily twice as heavy? As larger objects are typically heavier than smaller ones, one might assume humans use such heuristics in preparing to lift novel objects if other informative cues (e.g., material, previous lifts) are unavailable. However, it is also known that humans are sensitive to statistical properties of our environments, and that such sensitivity can bias perception. Here we asked whether statistical regularities in properties of liftable, everyday objects would bias human observers’ predictions about objects’ weight relationships. We developed state-of-the-art computer vision techniques to precisely measure the volume of everyday objects, and also measured their weight. We discovered that for liftable man-made objects, “twice as large” doesn’t mean “twice as heavy”: Smaller objects are typically denser, following a power function of volume. Interestingly, this “smaller is denser” relationship does not hold for natural or unliftable objects, suggesting some ideal density range for objects designed to be lifted. We then asked human observers to predict weight relationships between novel objects without lifting them; crucially, these weight predictions quantitatively match typical weight relationships shown by similarly-sized objects in everyday environments. These results indicate that the human brain represents the statistics of everyday objects and that this representation can be quantitatively abstracted and applied to novel objects. Finally, that the brain possesses and can use precise knowledge of the nonlinear association between size and weight carries important implications for implementation of forward models of motor control in artificial systems.

We propose a method for dense three-dimensional surface reconstruction that leverages the strengths of shapebased approaches, by imposing regularization that respects the geometry of the surface, and the strength of depthmap-based stereo, by avoiding costly computation of surface topology. The result is a near real-time variational reconstruction algorithm free of the staircasing artifacts that affect depth-map and plane-sweeping approaches. This is made possible by exploiting the gauge ambiguity to design a novel representation of the regularizer that is linear in the parameters and hence amenable to be optimized with stateof-the-art primal-dual numerical schemes.

In deflectometry, the shape of mirror objects is recovered from distorted images of a calibrated scene. While remarkably high accuracies are achievable, state-of-the-art methods suffer from two distinct weaknesses: First, for mainly constructive reasons, these can only capture a few square centimeters of surface area at once. Second, reconstructions are ambiguous i.e. infinitely many surfaces lead to the same visual impression. We resolve both of these problems by introducing the first multiview specular stereo approach, which jointly evaluates a series of overlapping deflectometric images. Two publicly available benchmarks accompany this paper, enabling us to numerically demonstrate viability and practicability of our approach

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