Topological descriptors for 3D surface analysis

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for a 2D cubical filtration. In the next step we investigate different topological descriptors and measure their ability to discriminate structurally different 3D surface patches. We evaluate their sensitivity to different parameters and compare the performance of the resulting topological descriptors to alternative (non-topological) descriptors. We present a comprehensive evaluation that shows that topological descriptors are (i) robust, (ii) yield state-of-the-art performance for the task of 3D surface analysis and (iii) improve classification performance when combined with non-topological descriptors.Comment: 12 pages, 3 figures, CTIC 201

Are Aquinas and Whitehead Metaphorical and Analogical All the Way Down?

The paper argues from the perspective of a significant strand of interpretation of Aquinas and from insights in cognitive linguistics that a fruitful dialogue between Whitehead and Thomism needs to take into account that metaphysics and talk about God are metaphorical and analogical all the way down. Cognitive linguistics provides an explanatory scheme for explaining how Aquinas’s tectonic use of analogy shifts the ground of our conventional fields of meanings to create space to conceptualize what otherwise would be beyond grasp and to make inferences possible that otherwise would be unthinkable. The essay concludes with a question, admittedly from a particular trajectory of Thomism and cognitive linguistics, about whether Whitehead’s conception of God adequately accounts for the radically metaphorical “imaginative leap” entailed in the Christian conception of God

Textbook Question Answering with Multi-modal Context Graph Understanding and Self-supervised Open-set Comprehension

In this work, we introduce a novel algorithm for solving the textbook question answering (TQA) task which describes more realistic QA problems compared to other recent tasks. We mainly focus on two related issues with analysis of the TQA dataset. First, solving the TQA problems requires to comprehend multi-modal contexts in complicated input data. To tackle this issue of extracting knowledge features from long text lessons and merging them with visual features, we establish a context graph from texts and images, and propose a new module f-GCN based on graph convolutional networks (GCN). Second, scientific terms are not spread over the chapters and subjects are split in the TQA dataset. To overcome this so called "out-of-domain" issue, before learning QA problems, we introduce a novel self-supervised open-set learning process without any annotations. The experimental results show that our model significantly outperforms prior state-of-the-art methods. Moreover, ablation studies validate that both methods of incorporating f-GCN for extracting knowledge from multi-modal contexts and our newly proposed self-supervised learning process are effective for TQA problems.Comment: ACL2019 Camera-read

Hierarchical stack filtering : a bitplane-based algorithm for massively parallel processors

With the development of novel parallel architectures for image processing, the implementation of well-known image operators needs to be reformulated to take advantage of the so-called massive parallelism. In this work, we propose a general algorithm that implements a large class of nonlinear filters, called stack filters, with a 2D-array processor. The proposed method consists of decomposing an image into bitplanes with the bitwise decomposition, and then process every bitplane hierarchically. The filtered image is reconstructed by simply stacking the filtered bitplanes according to their order of significance. Owing to its hierarchical structure, our algorithm allows us to trade-off between image quality and processing time, and to significantly reduce the computation time of low-entropy images. Also, experimental tests show that the processing time of our method is substantially lower than that of classical methods when using large structuring elements. All these features are of interest to a variety of real-time applications based on morphological operations such as video segmentation and video enhancement

Persistent Homology of Attractors For Action Recognition

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system. We reconstruct the phase-space of time series corresponding to actions using time-delay embedding, and compute the persistent homology of the phase-space reconstruction. In order to better represent the topological properties of the phase-space, we incorporate the temporal adjacency information when computing the homology groups. The persistence of these homology groups encoded using persistence diagrams are used as features for the actions. Our experiments with action recognition using these features demonstrate that the proposed approach outperforms other baseline methods.Comment: 5 pages, Under review in International Conference on Image Processin

Quantifiers on languages and codensity monads

This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a corresponding Reutenauer-type theorem. Our main tools are codensity monads and duality theory. Our construction hinges on a measure-theoretic characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that the Vietoris monad on Boolean spaces is the codensity monad of the finite powerset functor.Comment: 30 pages. Presentation improved and details of several proofs added. The main results are unchange

Use of colour for hand-filled form analysis and recognition

Colour information in form analysis is currently under utilised. As technology has advanced and computing costs have reduced, the processing of forms in colour has now become practicable. This paper describes a novel colour-based approach to the extraction of filled data from colour form images. Images are first quantised to reduce the colour complexity and data is extracted by examining the colour characteristics of the images. The improved performance of the proposed method has been verified by comparing the processing time, recognition rate, extraction precision and recall rate to that of an equivalent black and white system