A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves

Given a real valued function f(X,Y), a box region B_0 in R^2 and a positive epsilon, we want to compute an epsilon-isotopic polygonal approximation to the restriction of the curve S=f^{-1}(0)={p in R^2: f(p)=0} to B_0. We focus on subdivision algorithms because of their adaptive complexity and ease of implementation. Plantinga and Vegter gave a numerical subdivision algorithm that is exact when the curve S is bounded and non-singular. They used a computational model that relied only on function evaluation and interval arithmetic. We generalize their algorithm to any bounded (but possibly non-simply connected) region that does not contain singularities of S. With this generalization as a subroutine, we provide a method to detect isolated algebraic singularities and their branching degree. This appears to be the first complete purely numerical method to compute isotopic approximations of algebraic curves with isolated singularities

Discriminatively Trained Latent Ordinal Model for Video Classification

We study the problem of video classification for facial analysis and human action recognition. We propose a novel weakly supervised learning method that models the video as a sequence of automatically mined, discriminative sub-events (eg. onset and offset phase for "smile", running and jumping for "highjump"). The proposed model is inspired by the recent works on Multiple Instance Learning and latent SVM/HCRF -- it extends such frameworks to model the ordinal aspect in the videos, approximately. We obtain consistent improvements over relevant competitive baselines on four challenging and publicly available video based facial analysis datasets for prediction of expression, clinical pain and intent in dyadic conversations and on three challenging human action datasets. We also validate the method with qualitative results and show that they largely support the intuitions behind the method.Comment: Paper accepted in IEEE TPAMI. arXiv admin note: substantial text overlap with arXiv:1604.0150

Anticipation in Human-Robot Cooperation: A Recurrent Neural Network Approach for Multiple Action Sequences Prediction

Close human-robot cooperation is a key enabler for new developments in advanced manufacturing and assistive applications. Close cooperation require robots that can predict human actions and intent, and understand human non-verbal cues. Recent approaches based on neural networks have led to encouraging results in the human action prediction problem both in continuous and discrete spaces. Our approach extends the research in this direction. Our contributions are three-fold. First, we validate the use of gaze and body pose cues as a means of predicting human action through a feature selection method. Next, we address two shortcomings of existing literature: predicting multiple and variable-length action sequences. This is achieved by introducing an encoder-decoder recurrent neural network topology in the discrete action prediction problem. In addition, we theoretically demonstrate the importance of predicting multiple action sequences as a means of estimating the stochastic reward in a human robot cooperation scenario. Finally, we show the ability to effectively train the prediction model on a action prediction dataset, involving human motion data, and explore the influence of the model's parameters on its performance. Source code repository: https://github.com/pschydlo/ActionAnticipationComment: IEEE International Conference on Robotics and Automation (ICRA) 2018, Accepte

Univocity, Duality, and Ideal Genesis: Deleuze and Plato

In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and the Indefinite Dyad provides, in the later Plato, a unitary theoretical formalism accounting, by means of an iterated mixing without synthesis, for the structural origin and genesis of both supersensible Ideas and the sensible particulars which participate in them. As these commentators also argue, this duality furthermore provides a maximally general answer to the problem of temporal becoming that runs through Plato’s corpus: that of the relationship of the flux of sensory experiences to the fixity and order of what is thinkable in itself. Additionally, it provides a basis for understanding some of the famously puzzling claims about forms, numbers, and the principled genesis of both attributed to Plato by Aristotle in the Metaphysics, and plausibly underlies the late Plato’s deep considerations of the structural paradoxes of temporal change and becoming in the Parmenides, the Sophist, and the Philebus. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. These implications of Plato’s duality include not only those of the constitution of specific theoretical domains and problematics, but also implicate the reflexive problematic of the ideal determinants of the form of a unitary theory as such. We argue that the consequences of the underlying duality on the level of content are ultimately such as to raise, on the level of form, the broader reflexive problem of the basis for its own formal or meta-theoretical employment. We conclude by arguing for the decisive and substantive presence of a proper “Platonism” of the Idea in Deleuze, and weighing the potential for a substantive recuperation of Plato’s duality in the context of a dialectical affirmation of what Deleuze recognizes as the “only” ontological proposition that has ever been uttered. This is the proposition of the univocity of Being, whereby “being is said in the same sense, everywhere and always,” but is said (both problematically and decisively) of difference itself