Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognition

Online handwritten Chinese text recognition (OHCTR) is a challenging problem as it involves a large-scale character set, ambiguous segmentation, and variable-length input sequences. In this paper, we exploit the outstanding capability of path signature to translate online pen-tip trajectories into informative signature feature maps using a sliding window-based method, successfully capturing the analytic and geometric properties of pen strokes with strong local invariance and robustness. A multi-spatial-context fully convolutional recurrent network (MCFCRN) is proposed to exploit the multiple spatial contexts from the signature feature maps and generate a prediction sequence while completely avoiding the difficult segmentation problem. Furthermore, an implicit language model is developed to make predictions based on semantic context within a predicting feature sequence, providing a new perspective for incorporating lexicon constraints and prior knowledge about a certain language in the recognition procedure. Experiments on two standard benchmarks, Dataset-CASIA and Dataset-ICDAR, yielded outstanding results, with correct rates of 97.10% and 97.15%, respectively, which are significantly better than the best result reported thus far in the literature.Comment: 14 pages, 9 figure

FEAFA: A Well-Annotated Dataset for Facial Expression Analysis and 3D Facial Animation

Facial expression analysis based on machine learning requires large number of well-annotated data to reflect different changes in facial motion. Publicly available datasets truly help to accelerate research in this area by providing a benchmark resource, but all of these datasets, to the best of our knowledge, are limited to rough annotations for action units, including only their absence, presence, or a five-level intensity according to the Facial Action Coding System. To meet the need for videos labeled in great detail, we present a well-annotated dataset named FEAFA for Facial Expression Analysis and 3D Facial Animation. One hundred and twenty-two participants, including children, young adults and elderly people, were recorded in real-world conditions. In addition, 99,356 frames were manually labeled using Expression Quantitative Tool developed by us to quantify 9 symmetrical FACS action units, 10 asymmetrical (unilateral) FACS action units, 2 symmetrical FACS action descriptors and 2 asymmetrical FACS action descriptors, and each action unit or action descriptor is well-annotated with a floating point number between 0 and 1. To provide a baseline for use in future research, a benchmark for the regression of action unit values based on Convolutional Neural Networks are presented. We also demonstrate the potential of our FEAFA dataset for 3D facial animation. Almost all state-of-the-art algorithms for facial animation are achieved based on 3D face reconstruction. We hence propose a novel method that drives virtual characters only based on action unit value regression of the 2D video frames of source actors.Comment: 9 pages, 7 figure

Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning

Tail asymptotics of the Brownian signature

The signature of a path \gamma is a sequence whose n-th term is the order-n iterated integrals of \gamma. It arises from solving multidimensional linear differential equations driven by \gamma. We are interested in relating the path properties of \gamma with its signature. If \gamma is C1, then an elegant formula of Hambly and Lyons relates the length of \gamma to the tail asymptotics of the signature. We show an analogous formula for the multidimensional Brownian motion,with the quadratic variation playing a similar role to the length. In the proof, we study the hyperbolic development of Brownian motion and also obtain a new subadditive estimate for the asymptotic of signature, which may be of independent interest. As a corollary, we strengthen the existing uniqueness results for the signatures of Brownian motion

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe