Project Reading 8

MathPad2: A system for the creation and exploration of mathematical sketches

Citation:

LaViola, Jr., J. J., and Zeleznik, R. C. Mathpad2: A system for the creation and exploration of mathematical sketches. ACM Trans. Graph. 23, 3 (Aug. 2004), 432–440

Summary:

MathPad is the system that Identifies structure of a given mathematical expression by parsing and analysis of input string. It is a tool for Mathematical problem solving and visualization. Mathematical sketching, a novel, pen-based, modeless gestural interaction paradigm for mathematics problem solving is presented. With a mathematical sketch, 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. Mathematical sketching can also support computational tools for graphing,

manipulating and solving equations and initial feedback from a small user group of our mathematical sketching prototype application. MathPad2 introduces a new concept of combinations of handwritten mathematics and free-hand diagrams– that allow rapid animated visualization of mathematical formulations.

Discussion:

There is a restriction of the current prototype to closed-form expressions while drawing mathematical sketches if you need to use MathPad. Thus, the restriction does not make it for generic people. I think drawing restrictions should not be posed while making a system whose base is sketching.

Project Reading 7

                   MathBrush: A Case Study for Pen-based Interactive Mathematics

Citation:

Labahn, G., Lank, E., Marzouk, M., Bunt, A., MacLean, S., and Tausky, D. Mathbrush: A case study for pen-based interactive mathematics. In Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling, Eurographics Association (2008), 143–150.

Summary:

MathBrush recognizes mathematical expressions and facilitates problem solving using backend computer algebra systems. Current generations of computer algebra systems require users to transform two-dimensional math expressions into one-dimensional strings, to master complex sets of commands. Then analysis can be done on the output strings. MathBrush provides a pen-based interface to many of the features of computer algebra systems. The observations in this paper validate aspects of the current design of MathBrush, suggest areas for refinement, and inform the design of future pen-math systems. 

Discussion:

For MathBrush to be used, users need to modify their writing to adjust to the tolerances of recognition. The adaptations included slowing down the timing, taking additional care with symbol spacing, and altering the way that we draw certain characters. These are very basic writing techniques and we should be developing a system which takes care of these and not changes these. Thus, this aspect of the paper should be improved in my view.

Project Reading 6

MathPaper: Mathematical Sketching with Fluid Support for Interactive Computation

Citation:

Zeleznik, R., Miller, T., Li, C., and Laviola Jr, J. J. Mathpaper: Mathematical sketching with fluid support for interactive computation. In Smart Graphics, Springer (2008), 20–32.

Summary:

This paper presents a framework called MathPaper. It represents a system for fluid pen-based entry and editing of mathematics which also has the support for interactive computation. 

Writing on MathPaper interface is just like writing on a paper, in which multiple mathematical expressions and even algorithms can be entered anywhere on the page. It also talks about modification of Mathematical expressions using simple deletion and dragging gestures along with real-time recognition and computation feedback. 

MathPaper also supports extended notations and gestures for controlling computational assistance, simplifying input, and entering algorithms, making MathPaper a user-friendly system for mathematical sketching and computation.

Discussion:

This paper also presents the idea of writing mathematical equations on paper and not on the computer, which is the idea we are trying to work on in our term project. It also talks about modification of mathematical expression modification which we are also performing in our project.

Project Reading 5

Designing a Sketch Recognition Front-End: User Perception of Interface Elements

Citation:

Wais, P., Wolin, A., and Alvarado, C. Designing a sketch recognition front-end: User perception of interface elements. In Proceedings of the 4th Eurographics Workshop on Sketch-based Interfaces and Modeling, SBIM ’07, ACM (New York, NY, USA, 2007), 99–106.

Summary:

This paper focusses on presenting a user study which investigates critical sketch recognition user Interface issues in systems that recognize hand-drawn diagrams. There are four critical sketch recognition user interface issues:

1) how users integrate the process of triggering recognition into their work.

2) when users prefer to indicate which portions of the diagram should be recognized.

3) how users prefer to receive recognition feedback.

4) and how users perceive recognition errors.

The paper believes that programs that can recognize students’ hand-drawn diagrams can revolutionize education. This is because they break down the barriers between diagram creation and simulation. This paper thus focusses on understanding how to support this new interaction paradigm from a user’s perspective.

Discussion:

The paper presents a very well conducted user study to understand the drawbacks and limitations of the exisiting systems. They have shown the data for Electrical circuits for the user study. It would have been really helpful to perform the user study in any other domain also.

Project Reading 4

Citation:

LogicPad: A Pen-Based Application for Visualization and Verification of Boolean Algebra. Kang, B., and LaViola, J. Logicpad: A pen-based application for visualization and verification of boolean algebra. In Proceedings of the 2012 ACM International Conference on Intelligent User Interfaces, IUI ’12, ACM (New York, NY, USA, 2012), 265–268. 

Summary:

The paper presents a framework called LogicPad, which a pen-based application for boolean algebra

visualization. It lets users manipulate boolean function representations through handwritten symbol and gesture recognition. It also has a drag-and-drop interface which makes interaction with the interface much easier. LogicPad’s user interface and the general algorithm are discussed in the paper which are used for verifying the equivalence of three different boolean function representations: boolean expressions, truth tables, and logic gate diagrams. A user study is also conducted by the authors evaluating LogicPad’s user interface, visualization techniques, and overall performance.

Discussion:

As per the results, visualizations were generally well-liked and verification results matched

user expectations, which is pretty good. The sketching area on which the users write as they normally would using pen and paper, is very intuitive and which we are trying to follow in our project too.

Project Reading 3

Citation:

A Handwriting-Based Equation Editor. Written by: Steve Smithies, Kevin Novins, James Arvo.

Summary:

Equation editing systems relying on either textbased equation description languages or on interactive

construction by means of structure templates and menus are tedious to use, even for experts, because the user is forced to “parse” the expressions mentally before they are entered. The system described below is a prototype equation editor that is based on handwriting recognition and automatic equation

parsing. 

The recognition system performs Character Recognition, Stroke grouping and Equation parsing. Parsing uses LATEX like notation.The main drawbacks of a graph grammar approach are

the number and complexity of subgraph searches. The system also provides a basic User interface for ease of use. It also provides correcting of stroke grouping errors and correcting of character recognition errors. The next step is providing correction of Equation parsing errors. This system provides a natural and familiar interaction method or recognizing equations.

Discussion:

The time taken for parsing simple formulæ is less than two seconds, though more complicated formulæ may take twenty seconds or more. This time taken for parsing is very less and shows the efficiency this system has.

Project Reading 2

Recognition and retrieval of mathematical expressions

Citation:

Recognition and retrieval of mathematical expressions. Written by: Richard Zanibbi , Dorothea Blostein.

Summary:
This paper surveys recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning).
The problems arising in Math Notation recognition are:
1) Expression Detection
2) Symbol Extraction or Symbol Recognition
3) Layout Analysis
4) Mathematical content Interpretation

It creates two kinds of trees for equation recognition: Symbol layout tree and Operator tree. The following problems arise in retrieval of Math notation:
1) Query languages and query formulation
2) Normalization
3) Indexing and matching
4) Relevance feedback

In solving the ambiguity of mathematical expressions, we first need to understand the meaning of what do each of the symbols represent.

Discussion:
This paper has given many future work ideas. Also, while doing our project, we felt on the same lines as the author (that solving the ambiguity in Math expressions, we need to understand meaning of each symbol). The use of various tools like MathML and Latex is very intuitive.