One of the primary research themes in the IS&UE lab is creating new and innovative pen-centric user interfaces and applications. The main focus of our work in pen computing is mathematical sketching, the ability to associate handwritten mathematics and drawings together to create illustrations that assist users in learning and understanding science and mathematical concepts. We are also interested in learning how users are affected by the pen-centric interfaces we develop and whether the educational applications we create are pedagogically effective. In addition, we are exploring how multi-touch interfaces can be used in mathematics and in improving workflow efficiency.
Diagrams and illustrations are frequently used to help explain mathematical concepts. Students often create them with pencil and paper as an intuitive aid in visualizing relationships among variables, constants, and functions, and use them as a guide in writing the appropriate mathematics to solve the problem. However, such static diagrams generally assist only in the initial formulation of the required mathematics, not in "debugging" or problem analysis. This can be a severe limitation, even for simple problems with a natural mapping to the temporal dimension or problems with complex spatial relationships.
Mathematical sketching is a novel, pen-based, gestural interaction paradigm for mathematics problem solving, designed to overcome these limitations. Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; however, with mathematical sketching, users can also leverage their physical intuition by watching their hand-drawn diagrams animate in response to continuous or discrete parameter changes in their written formulas. Diagram animation is driven by implicit associations that are inferred, either automatically or with gestural guidance, from mathematical expressions, diagram labels and drawing elements.
Math Boxes is a novel pen-based user interface for simplifying the task of hand writing difficult mathematical expressions. Visible bounding boxes around certain subexpressions are automatically generated as the system detects specific relationships including superscripts, subscripts, and fractions. Subexpressions contained in a box can then be extended by adding new terms directly into its given bounds. Upon accepting new characters, box boundaries are dynamically resized and neighboring terms are translated to make room for the larger box. Feedback on structural recognition is given via the boxes themselves. We also provide feedback on character recognition by morphing the user's individual characters into a cleaner version stored in our ink database.
AnalyticalInk is a novel math learning environment prototype that uses a semantic graph as the knowledge representation of algebraic and geometric word problems. The system solves math problems by reasoning upon the semantic graph and automatically generates conceptual and procedural scaffoldings in sequence. We further introduce a step-wise tutoring framework, which can check students’ input steps and provide the adaptive scaffolding feedback. Based on the knowledge representation, AnalyticalInk highlights keywords that allow users to further drag them onto the workspace to gather insight into the problem’s initial conditions. The system simulates a pen-and-paper environment to let users input both in algebraic and geometric workspaces. We conducted an usability evaluation to measure the effectiveness of AnalyticalInk. We found that keyword highlighting and dragging is useful and effective toward math problem solving. Answer checking in the tutoring component is useful. In general, our prototype shows the promise in helping users to understand geometrical concepts and master algebraic procedures under the problem solving.
QuickDraw is a prototype sketch-based drawing tool that facilitates drawing of precise geometry diagrams that are often drawn by students and academics in several scientific disciplines. Quickdraw can recognize sketched diagrams containing components such as line segments and circles, infer geometric constraints relating recognized components, and use this information to beautify the sketched diagram. Beautification is based on a novel algorithm that iteratively computes various sub-components of the components using an extensible set of deductive rules.
LogicPad is a pen-based application for boolean algebra visualization that lets users manipulate boolean function representations through handwritten symbol and gesture recognition coupled with a drag-and-drop interface. LogicPad's user interface has three three different boolean function representations: boolean expressions, truth tables, and logic gate diagrams, and can verify the equivalence of the different representations.
CSTutor is a pen-based application for data structure visualization that lets users manipulate data structures through the recognition of handwritten symbols and gestures as well as edit the corresponding code. The UI consists of a sketching area where the user can draw a data structure in a way that is as natural as pen and paper. Running in parallel with the visualization is a code view where users can make changes to the source code and add functions which manipulate the data structure on the canvas in real time.
Sketch-based intelligent tutoring is a new approach for creating dynamic illustrations to assist in the understanding of concepts in physics and mathematics using pen-based interaction. This approach builds upon mathematical sketching by combining the ability to make associations between handwritten mathematics and free-form drawings with an underlying physics engine. This combination lets users create animations without having to directly specify object behavior with position functions through time, yet still supports writing the mathematics needed to formulate a problem. This functionality significantly expands the capabilities of mathematical sketching to support a wider variety of dynamic illustrations.
MathPad^{2} is a pen-based application prototype for creating mathematical sketches. Using a modeless gestural interface, it lets users make dynamic illustrations by associating handwritten mathematics with free-form drawings and provides a set of tools for graphing and evaluating mathematical expressions and solving equations.
Recently, $-family recognizers have become prevalent for sketch recognition, and for good reason. They are easily implemented and accurate. However, there is a trade off between accuracy and execution time. We have explored techniques of minimizing this tradeoff using minimalist recognizers and intelligent prototype selection.
Training gesture recognizers with synthetic data generated from real gestures is a well known and powerful technique that can significantly improve recognition accuracy. We introduce a novel technique called gesture path stochastic resampling (GPSR) that is computationally efficient, has minimal coding overhead, and yet despite its simplicity is able to achieve higher accuracy than competitive, state-of-the-art approaches. GPSR generates synthetic samples by lengthening and shortening gesture subpaths within a given sample to produce realistic variations of the input via a process of nonuniform resampling. As such, GPSR is an appropriate rapid prototyping technique where ease of use, understandability, and efficiency are key. A demonstration of this technique is available here.
The $-family of recognizers ($1, Protractor $N, $P, 1¢, and variants) are an easy to understand, easy to implement, accurate set of gesture recognizers designed for non-experts and rapid prototyping. Penny Pincher achieves high accuracy by being able to process a large number of templates in a short amount of time. If, for example, a recognition task is given a 50µs budget to complete its work, a fast recognizer that can process more templates within this constraint can potentially outperform its rival recognizers. Penny Pincher achieves this goal by reducing the template matching process to merely addition and multiplication, by avoiding translation, scaling, and rotation; and by avoiding calls to expensive geometric functions. Despite Penny Pincher’s deceptive simplicity, our recognizer, with a limited number of templates, still performs remarkably well.
We explore the benefits of intelligent prototype selection for $-family recognizers. Currently, the state of the art is to randomly select a subset of prototypes from a dataset without any processing. This results in reduced computation time for the recognizer, but also increases error rates. We propose applying optimization algorithms, specifically random mutation hill climb and a genetic algorithm, to search for reduced sets of prototypes that minimize recognition error. After a large scale evaluation, we found that error rates could be reduced compared to random selection and rapidly approached the baseline accuracies for a number of different $-family recognizers. Penny Pincher, in particular, responded well to prototype selection.
The pen-and-paper interface metaphor that pen-based computers provide make pen-based interfaces both natural and expressive. However, these interfaces can also be difficult to use without proper feedback and guidance in understanding how to perform the various gestures and pen-based commands for a particular application. This project focuses on understanding we can develop tools to assist users when working with pen-based UIs.
Researchers hypothesize pen-based interfaces are the input method of choice for structured 2D languages, as they are natural for users. In our research, we seek to understand how users feel about these interfaces and whether they are indeed ideal for structured 2D languages.
Mathematical handwriting recognition is an important method of mathematics input for computers. While strides in recognition have been made in recent years, recognition is still at a level where mistakes are common and often inexplicable from the user's point-of-view. As a result, recognition mistakes can cause user distraction and frustration. We examine how user preference for real-time or batch recognition mode is affected by recognition accuracy and the number of expressions entered. Our results show that users prefer real-time recognition when working with multiple expressions; however, with high accuracy recognition, users did not prefer one recognition mode over the other.
The focus of this project is to explore multi-touch input. We are currently investigating how this input modality can be used for interacting with 3D objects on a 2D display, and how it can be combined with pen-input for entering and manipulating handwritten mathematical expressions.
Although multi-touch interaction in 2D has become widespread on mobile devices, intuitive ways to interact with 3D objects has not been thoroughly explored. We present a study on natural and guided multi-touch interaction with 3D objects on a 2D multi-touch display. Specifically, we focus on interactions with 3D objects that have either rotational, tightening, or switching components on mechanisms that might be found in mechanical operation or training simulations.
SetPad is a new application prototype that lets computer science students explore discrete math problems by sketching set expressions using pen-based input. Students can manipulate the expressions interactively with the tool via pen or multi-touch interface. Likewise, discrete mathematics instructors can use SetPad to display and work through set problems via a projector to better demonstrate the solutions to the students. We discuss the implementation and feature set of the application, as well as results from a formal user study measuring the effectiveness of the tool for students solving set proof problems. The results indicate that SetPad allows for efficient solutions to proof problems, and has the potential to have a positive impact when used as an individual student application or as an instructional tool.