From Facial Parts Responses to Face Detection: A Deep Learning Approach

In this paper, we propose a novel deep convolutional network (DCN) that achieves outstanding performance on FDDB, PASCAL Face, and AFW. Specifically, our method achieves a high recall rate of 90.99% on the challenging FDDB benchmark, outperforming the state-of-the-art method by a large margin of 2.91%. Importantly, we consider finding faces from a new perspective through scoring facial parts responses by their spatial structure and arrangement. The scoring mechanism is carefully formulated considering challenging cases where faces are only partially visible. This consideration allows our network to detect faces under severe occlusion and unconstrained pose variation, which are the main difficulty and bottleneck of most existing face detection approaches. We show that despite the use of DCN, our network can achieve practical runtime speed.Comment: To appear in ICCV 201

Deformable Part Models are Convolutional Neural Networks

Deformable part models (DPMs) and convolutional neural networks (CNNs) are two widely used tools for visual recognition. They are typically viewed as distinct approaches: DPMs are graphical models (Markov random fields), while CNNs are "black-box" non-linear classifiers. In this paper, we show that a DPM can be formulated as a CNN, thus providing a novel synthesis of the two ideas. Our construction involves unrolling the DPM inference algorithm and mapping each step to an equivalent (and at times novel) CNN layer. From this perspective, it becomes natural to replace the standard image features used in DPM with a learned feature extractor. We call the resulting model DeepPyramid DPM and experimentally validate it on PASCAL VOC. DeepPyramid DPM significantly outperforms DPMs based on histograms of oriented gradients features (HOG) and slightly outperforms a comparable version of the recently introduced R-CNN detection system, while running an order of magnitude faster

Analogues Between Leibniz\u27s Harmonic Triangle and Pascal\u27s Arithmetic Triangle

This paper will discuss the analogues between Leibniz\u27s Harmonic Triangle and Pascal\u27s Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya\u27s perspective. The topics presented in this paper will show that Pascal\u27s triangle and Leibniz\u27s triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal\u27s Arithmetic Triangle can be used to construct Leibniz\u27s Harmonic Triangle and show how both triangles relate to combinatorics and arithmetic through the coefficients of the binomial expansion. Furthermore, combinatorics plays an increasingly important role in mathematics, starting when students enter high school and continuing on into their college years. Students become familiar with the traditional arguments based on classical arithmetic and algebra, however, methods of combinatorics can vary greatly. In combinatorics, perhaps the most important concept revolves around the coefficients of the binomial expansion, studying and proving their properties, and conveying a greater insight into mathematics

Pascal’s wager: tracking an intended reader in the structure of the argument

Pascal’s wager is the name of an argument in favor of belief in God presented by Blaise Pascal in §233 of Thoughts. Ian Hacking (1972) pointed out that Pascal’s text involves three different versions of the argument. This paper proceeds from this identification, but it concerns an examination of the rhetorical strategy realized by Pascal’s argumentation. The final form of Pascal’s argument is considered as a product that could be established only through a specific process of persuasion led with respect to an intended reader with a particular set of initial beliefs. The text uses insights from the pragma‐dialectical approach to argumentation, especially the concept of rhetorical effectiveness of particular choices from the topical potential. The argumentation structure of Pascal’s wager is considered to be a reflection of the anticipated course of dialogue with the reader critically testing the sustainability of Pascal’s standpoint “You should believe in God”. Based on the argumentation reconstruction of three versions of the argument, Pascal’s idea of opponent/audience is identified. A rhetorical analysis of the effects of his argumentative strategy is proposed. The analysis is based on two perspectives on Pascal’s argument: it examines the strategy implemented consistently by all arguments and the strategy of a formulation of different versions of the wager