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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? 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Geometric Analysis of Observability of Target Object Shape Using Location-Unknown Distance Sensors
Hiroshi Saito, Hirotada Honda · 2017-05-15 · via cs.IT updates on arXiv.org

We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis using geometric probability, we discuss the observability of these parameters: which parameters we can estimate and what conditions are required to estimate them. For a convex target object, its size and perimeter length are observable, and other parameters are not observable. For a general polygon target object, convexity in addition to its size and perimeter length is observable. Parameters related to a concave vertex can be observable when some conditions are satisfied. We also propose a method for estimating the convexity of a target object and the perimeter length of the target object.

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