Ernesto Tapia

Recognition of on-line handwritten mathematical formulas in the E-chalk system

In this article, we present a system for the recognition ofon-line handwritten mathematical formulas which is usedin the electronic chalkboard (E-chalk), a multimedia systemfor distance-teaching. We discuss the classification of symbolsand the construction of the tree of spatial relationshipsamong them. The classification is based on support vectormachines and the construction of formulas is based onbaseline structure analysis.

Recognition of On-line Handwritten Mathematical Expressions Using a Minimum Spanning Tree Construction and Symbol Dominance

We present a structural analysis method for the recognition of on-line handwritten mathematical expressions based on a minimum spanning tree construction and symbol dominance. The method handles some layout irregularities frequently found in on-line handwritten formula recognition systems, like symbol overlapping and association of arguments of sum-like operators. It also handles arguments of operators with non-standard layouts, as well as tabular arrangements, like matrices.

E-Chalk: a lecture recording system using the chalkboard metaphor

This article describes a system that produces web based learning modules as a by‐product of regular classroom teaching. The lecturer uses a pen sensitive display in place of the traditional chalkboard. In addition to drawings, the electronic chalkboard handles a range of multimedia elements from the Internet. The system records all actions and provides both a live transmission and a replay of the lecture from the web. Remote students follow the lecture looking at the dynamic board content and listening to the recorded voice of the instructor. Several use cases of the system as well as a systematic evaluation in two universities are presented.

A note on the computation of high-dimensional integral images

The integral image approach allows optimal computation of Haar-based features for real-time recognition of objects in image sequences. This paper describes a generalization of the approach to high-dimensional images and offers a formula for optimal computation of sums on high-dimensional rectangles.

Recognition of on-line handwritten mathematical expressions in the E-Chalk system - an extension

This article introduces the new version of our system for the recognition of on-line handwritten mathematical expressions. The previous version was capable to recognize the most common mathematical expressions, such as expressions of calculus, following the usual mathematical conventions. This version improves and extends our technique, allowing the recognition of structures described by tabular and multiline arrangements, such as matrices and systems of equations. The recognition results are stored in a composite of symbols, which are used by computer algebra systems for algebraic computations, and Junction plotting. The system is embedded as an intelligent assistant in the electronic chalkboard (E-Chalk), a system for the live transmission and storage of lectures.

WEB BASED LECTURES PRODUCED BY AI SUPPORTED CLASSROOM TEACHING

This article presents a system that maps classroom lectures directly into web based education lessons. In the classroom, the lecturer writes on a wide, pen sensitive display. The system tracks all actions and makes it possible for the lecture to be replayed from the web any time. The remote viewer can follow the progress of the lecture: Audio, the creation of the board content, and an optional video image of the instructor is transmitted. In addition to usual drawing functionality the board can handle a range of multimedia elements from the Internet. The board can integrate different kinds of modules, invoked by board drawings. One of these modules is described here: A computer algebra system that evaluates mathematical expressions or plots functions is placed at the lecturers disposal by a handwriting recognition.

Quantile Linear Algorithm for Robust Binarization of Digitalized Letters

We describe a threshold-based local algorithm for image binarization. The main idea is to compute a transition energy using pixel value differences taken from a neighborhood around the pixel of interest. By filtering the pixels with low positive and negative energy, we keep two subsets in the neighborhood, corresponding to higher positive and negative energy values. The binarization threshold is calculated using a statistical model of the high energy pixels. Experiments show that this new approach is faster and better than current state-of-the-art algorithms.

Web Based Education as a Result of AI Supported Classroom Teaching

This paper presents a system that maps classroom lectures directly into web based education lessons. In the classroom, the lecturer writes on a wide, pen sensitive display. The system tracks all actions and makes it possible for the lecture to be replayed from the web any time. The remote viewer can follow the progress of the lecture: Audio, the creation of the board content, and an optional video image of the instructor is transmitted. In addition to usual drawing functionality the board can handle a range of multimedia elements from the Internet. The board can integrate all kinds of modules, invoked by board drawings. One of these modules is described here: A computer algebra system that evaluates mathematical expressions or plots functions is placed at the lecturers disposal by a handwriting recognition.

Recognition of On-Line Handwritten Commutative Diagrams

We present a method for the recognition of on-line hand-written commutative diagrams. Diagrams are formed with arrows that join relatively simple mathematical expressions. Diagram recognition consists in grouping isolated symbols into simple expressions, recognizing the arrows that join such expressions, and finding the layout that best describes the diagram. We model the layout of the diagram with a grid that optimally fits a tabular arrangement of expressions. Our method maximizes a linear function that mea-sures the quality of our layout model. The recognition results are translated into the LaTeX library xy-pic.

An Incremental Fuzzy Algorithm for the Balance of Humanoid Robots

Humanoid robots base their appearance on the human body (Goddard et al., 1992; Kanehira et al., 2002; Konno et al., 2000). Minimalist constructions have at least a torso with a head, arms or legs, while more elaborated ones include devices that assemble, for example, human face parts, such as eyes, mouth, and nose, or even include materials similar to skin. Humanoid robots are systems with a very high complexity, because they aim to look like humans and to behave as they do. Mechanical control, sensing, and adaptive behaviour are the constituting logical parts of the robot that allow it to “behave” like a human being. Normally, researchers study these components by modelling only a mechanical part of the humanoid robot. For example, artificial intelligence and cognitive science researches consider the robot from the waist up, because its visual sensing is located in its head, and its behavior with gestures normally uses its face or arms. Some engineers are mostly interested in the autonomy of the robot and consider it from the waist down. They develop mathematical models that control the balance of the robot and the movement of its legs (Miller, 1994; Yamaguchi et al., 1999; Taga et al., 1991), allowing the robot to walk, one of the fundamental behaviours that characterizes human beings. Examples of such mathematical models are static and dynamic walking. The static walking model controls the robot to maintain its center of gravity (COG) inside a stable support region, while the dynamic walking model maintains the zero moment point (ZMP) inside the support region. Kajita et al. (1992) designed and developed an almost ideal 2-D model of a biped robot. He supposed, for simplicity, that the robots COG moves horizontally and he developed a control law for initiation, continuation and termination of the walking process. Zhen and Shen (1990) proposed a scheme to enable robot climbing on inclined surfaces. Force sensors placed in the robots feet detect transitions of the terrain type, and motor movements correspondingly compensate the inclination of robot. The models mentioned above can be, however, computationally very expensive, and prohibitive for its implementation in microcontrollers. Control algorithms for a stable walking must be sufficiently robust and smooth, to accomplish a balance correction without putting in risk the mechanical stability of the robot. This could be resolved by using a controller that modifies its parameters according to a