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Contact pressure between the human body and its surroundings has important implications. For example, it plays a role in comfort, safety, posture, and health. We present a method that infers contact pressure between a human body and a mattress from a depth image. Specifically, we focus on using a depth image from a downward facing camera to infer pressure on a body at rest in bed occluded by bedding, which is directly applicable to the prevention of pressure injuries in healthcare. Our approach involves augmenting a real dataset with synthetic data generated via a soft-body physics simulation of a human body, a mattress, a pressure sensing mat, and a blanket. We introduce a novel deep network that we trained on an augmented dataset and evaluated with real data. The network contains an embedded human body mesh model and uses a white-box model of depth and pressure image generation. Our network successfully infers body pose, outperforming prior work. It also infers contact pressure across a 3D mesh model of the human body, which is a novel capability, and does so in the presence of occlusion from blankets.

Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modeled as an elongating path or series of segments, without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by expanding the area around the completed elongated path. Modeling expansion in this way can lead to contradictions in the physical plausibility of the resulting surface and to uncertainty about how the object reached certain regions of space. Here, we introduce fiber walks as a self-avoiding random walk model for tip-driven growth processes that includes lateral expansion. In 2D, the fiber walk takes place on a square lattice and the space occupied by the fiber is modeled as a lateral contraction of the lattice. This contraction influences the possible subsequent steps of the fiber walk. The boundary of the area consumed by the contraction is derived as the dual of the lattice faces adjacent to the fiber. We show that fiber walks generate fibers that have well-defined curvatures, and thus enable the identification of the process underlying the occupancy of physical space. Hence, fiber walks provide a base from which to model both the extension and expansion of physical biological objects with finite thickness.

This paper describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalizations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The paper further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic formalism more readily accessible for future application in the physical sciences. [ABSTRACT FROM AUTHOR]