Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem

Ajjanagadde, Ganesh; Thrampoulidis, Christos; Yedidia, Adam; Wornell, Gregory W.

doi:10.1109/icassp.2019.8682254

Cited by 3 publications

(3 citation statements)

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“…For instance, an important mathematical problem in computational imaging is to develop optimal coded apertures. In [1], their fundamental limits were characterized using Theorem 5.8, and a greedy algorithm that relies on the proof of this theorem was proposed. Also see [19] for a discussion of various problems in signal processing where Theorem 5.8 might come in handy.…”

Section: Applications and Extensions Of Nazarov's Resultsmentioning

confidence: 99%

Plank theorems and their applications: a survey

Verreault¹

2022

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Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics. Tarski's plank problem The genesis of plank problemsIn the 1930s, the mathematician and logician Alfred Tarski, who is known for his work on model theory and the Banach-Tarski paradox, among other things, proposed a problem that would change the face of discrete geometry. It is what we now call a plank problem. Conjecture 2.1 (Tarski [53], 1932). If C ⊂ R d is covered by a sequence of planks P 1 , P 2 . . . , P n , then the sum of the widths of the planks is at least w(C).Without loss of generality, we may consider a body of minimal width 1. Then, similarly to our answer to Question 1.1, it is obvious that we can cover a convex body of minimal width 1 with planks that have total width 1, by placing them perpendicularly to the hyperplanes that support the convex body. But can we do better? Tarski's conjecture says no. Partial solution to Tarski's problemTarski proved his conjecture for figures in which we can inscribe a disk centered at the origin. Note that the case of R 2 is not entirely covered by this partial result, since some convex figures, for example an equilateral triangle, have a width bigger than the diameter of their inscribed circle; yet, Tarski's arguments generalize to solids in which we can inscribe a ball centered at the origin. However, they do not work in higher dimensions because the proof relies on geometric characteristics of two (or three)-dimensional spaces. His proof is still interesting in its own right, so we include it by adapting the argument that was presented in [35]. Note that Tarski was inspired by a solution of Moese on a related problem first stated by Tarksi himself (read [42, Chapter 7] for a discussion on the history of this problem and a translation of the related papers of Tarski and Moese).The demonstration relies essentially on a result of Archimedes in On the Sphere and Cylinder, often called "Archimedes' Hat-Box Theorem", which can be formulated as follows.Proposition 2.2. The lateral area of a spherical segment formed by the intersection of a sphere of radius r and two planes separated by distance d is 2πrd.

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Section: Applications and Extensions Of Nazarov's Resultsmentioning

confidence: 99%

Plank theorems and their applications: a survey

Verreault¹

2022

Preprint

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“…Under this model, assuming the occluder is an opaque object that completely blocks the light, the light transport matrix A can be defined as A ij = 0 if the occluder blocks the light coming from i-th pixel of the face image to j-th pixel of the observation plane, and A ij = 1/n otherwise. Here, the (1/n)-scaling ensures that the observed total power does not exceed the total power reflected from the face [56,3]. We illustrate representative images of shadows obtained with this model in Figure 3, where a rectangular occluder is simulated.…”

Section: Convolutional Model Of Occlusionmentioning

confidence: 99%

“…We simulate a rectangular occluder with a 512×512 image that contains a square with a diagonal length of 400 pixels. After proper scaling in pixel values to ensure the conservation of energy [3,56], we convolve this image with the rendered face images to obtain the shadow images, which we downsample to 128 × 128 resolution. Hence, we have n = 128 2 = 16384, i.e, each observation in the dataset is a 16384-dimensional vector.…”

Section: Supplementary Materials a Implementation Detailsmentioning

confidence: 99%

Can Shadows Reveal Biometric Information?

Medin¹,

Weiss²,

Durand³

et al. 2022

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We study the problem of extracting biometric information of individuals by looking at shadows of objects cast on diffuse surfaces. We show that the biometric information leakage from shadows can be sufficient for reliable identity inference under representative scenarios via a maximum likelihood analysis. We then develop a learning-based method that demonstrates this phenomenon in real settings, exploiting the subtle cues in the shadows that are the source of the leakage without requiring any labeled real data. In particular, our approach relies on building synthetic scenes composed of 3D face models obtained from a single photograph of each identity. We transfer what we learn from the synthetic data to the real data using domain adaptation in a completely unsupervised way. Our model is able to generalize well to the real domain and is robust to several variations in the scenes. We report high classification accuracies in an identity classification task that takes place in a scene with unknown geometry and occluding objects.

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