A. Grbavec and D. Blostein. Mathematics recognition using graph rewriting. In Proc. of ICDAR'95, pages 417-421, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....cases. For example, when there exist more than two symbols in an expression, spatial relationships among symbols can only be determined globally. In most cases, we have to locate the first symbol before other relationships can be identified accordingly. Fig. 4 shows an example. Several systems [18,20,29,41,42,62] have made extra effort in dealing with these problems. Fig. 4. Subscript and superscript relationships cannot be determined locally Superscript and subscript expressions usually appear in the upper right and lower right areas of another symbol. However, there are exceptions, for example, n C ....

....a parser using generalized twodimensional context free grammar to parse two dimensional structures like mathematical expressions. However, all discussions in that paper are limited to parsing in a theoretical sense with no real examples and experimental results shown. Grbavec and Blostein [20] used a graph rewriting approach to recognize mathematical expressions. Their model includes four phases: 1. The build phase constructs edges to represent spatial relationships between symbols. 2. The constrain phase applies domain knowledge to remove contradictions and resolve ambiguities. 3. ....

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A. Grbavec and D. Blostein. Mathematics recognition using graph rewriting. In ICDAR'95 [26], pages 417--421.

....VISUAL LANGUAGES 119 structed ASGs are used for interpretation and compilation purposes, whereas SRGs are used to layout and to display (render) visual language representations. Please note that SRGs may also be produced as the output of a scanning and pattern recognition process as described in [50]. Furthermore, it is sometimes desirable to manipulate SRGs using a low level graphics editor. A graph grammar parser is then responsible for recreating the new graph s derivation history. Abstract Syntax Graph (ASG) Derivation Spatial Relations Graph (SRG) Derivation translation ....

A. Grbavec and D. Blostein. Mathematics recognition using graph rewriting. In Third Int. Conf. on Document Image Analysis and Recognition, pages 417--421, Montreal, Canada, 1995.

....exponent and subscript. Pfei er [13] designed a parser for contextfree languages in order to parse two dimensional structures like mathematical expressions. However, all the discussions in that paper are limited to parsing in a theoretical sense with no real examples shown. Grbavec and Blostein [14] used a graph rewriting approach for the understanding of mathematical expressions. Their system made use of knowledge about notational conventions to avoid the need for backtracking. Other papers in the 1980s and 1990s investigated both the character recognition and structural analysis stages ....

A. Grbavec, D. Blostein, Mathematics recognition using graph rewriting, in Proceedings of the Third International Conference on Document Analysis and Recognition, Montreal, Canada, 1995, pp. 417}421.

....exponent and subscript. Pfeiffer [13] designed a parser for context free languages in order to parse two dimensional structures like mathematical expressions. However, all the discussions in that paper are limited to parsing in a theoretical sense with no real examples shown. Grbavec and Blostein [14] used a graph rewriting approach for the understanding of mathematical expressions. Their system made use of knowledge about notational conventions to avoid the need for backtracking. Other papers in the 1980s and 1990s investigated both the character recognition and structural analysis stages ....

A. Grbavec and D. Blostein, Mathematics recognition using graph rewriting, in ICDAR'95

....mentioned, once constructed ASGs are used for interpretation and compilation purposes, whereas SRGs are used to layout and to display (render) visual language representations. Please note that SRGs may also be produced as the output of a scanning and pattern recognition process as described in [57]. Furthermore, it is sometimes desirable to manipulate SRGs using a low level graphics editor. A graph grammar parser is then responsible for recreating the new graph s derivation history. 14 Abstract Syntax Graph (ASG) Derivation Spatial Relations Graph (SRG) Derivation translation ....

A. Grbavec and D. Blostein. Mathematics recognition using graph rewriting. In Third Int. Conf. on Document Image Analysis and Recognition, pages 417--421, Montreal, Canada, 1995.

....cases. For example, when there exist more than two symbols in an expression, spatial relationships among symbols can only be determined globally. In most cases, we have to locate the first symbol before other relationships can be identified accordingly. Figure 4 shows an example. Several systems [17, 18, 34, 35, 50] have made extra effort in dealing with these problems. Figure 4: Subscript and superscript relationships cannot be determined locally Superscript and subscript expressions usually appear in the upper right and lower right areas of another symbol. However, there are exceptions, for example, n ....

....using generalized two dimensional context free grammar in order to parse two dimensional structures like mathematical expressions. However, all discussions in that paper are limited to parsing in a theoretical sense with no real examples and experimental results shown. Grbavec and Blostein [18] used a graph rewriting approach to recognize mathematical expressions. Their model includes four phases: 1. The build phase constructs edges to represent spatial relationships between symbols. 2. The constrain phase applies domain knowledge to remove contradictions and resolve ambiguities. 3. ....

[Article contains additional citation context not shown here]

A. Grbavec and D. Blostein. Mathematics recognition using graph rewriting. In ICDAR'95

....exponent and subscript. Pfeiffer [21] designed a parser for context free languages in order to parse two dimensional structures like mathematical expressions. However, all the discussions in that paper are limited to parsing in a theoretical sense with no real examples shown. Grbavec and Blostein [9] used a graph rewriting approach for the understanding of mathematical expressions. Their system made use of knowledge about notational conventions to avoid the need for backtracking. Other papers in the 1980s and 1990s investigated both the character recognition and structural analysis stages ....

A. Grbavac and D. Blostein. Mathematics recognition using graph rewriting. In Proceedings of the Third International Conference on Document Analysis and Recognition, pages 417-- 421, Montreal, Canada, 1995.

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A. Grbavec and D. Blostein, "Mathematics Recognition Using Graph Rewriting," Third International Conference on Document Analysis and Recognition, Montreal, Canada, August 1995, pp. 417-421.

....preceding one. Most inputs are processed in near linear time. This is particularly impressive because DRACULAE handles handwritten inputs with irregular symbol placements. Many alternative approaches designed to cope with ambiguous layout, such as stochastic grammars [20] and graph transformation [21], involve extensive amounts of search or backtracking. DRACULAE currently recognizes a single dialect of mathematics notation, but has been constructed to allow multiple dialects to be accommodated in the future. Fig. 2 provides an overview of the processing performed by DRACULAE. Tree ....

A. Grbavec and D. Blostein, "Mathematics Recognition Using Graph Rewriting," Proc. Third Int'l Conf. Document Analysis and Recognition, pp. 417-421, 1995.

....problems is characterized by the following dimensions. The diagram notation A great diversity of diagram notations are in use. Recognition techniques have been developed for a variety of notations, including engineering drawings [21] 22] 33] 35] 72] mathematics notation [1] 10] 17] 25] [28] [71] music notation [4] 9] 23] 36] chemical structure diagrams [46] circuit diagrams [14] 37] 51] and line drawings [13] 52] 62] There is need for a classification or categorization of diagrams, to provide a vocabular for discussing the input domain of a diagram recognition system. ....

....graph (by adding a means of controlling when productions are to be applied) Both methods of using graph productions have been applied to diagram recognition. 6 The transformation approach has been applied to recognition of circuit diagrams [14] music notation [6] 23] 24] and math notation [28]. The graph grammar approach has been applied to recognition of engineering drawings [22] tables [61] and math notation [43] Most of these are research prototypes. However, the table recognition work by Rahgozar and Cooperman became part of a commercial product. 3.3 Stochastic Grammars Images ....

A. Grbavec, D. Blostein, "Mathematics Recognition Using Graph Rewriting," Third Intl. Conf. on Document Analysis and Recognition, Montreal, Aug. 1995, 417-421. 13

....Graph edges between files support cross referencing and version management. Graph rewrite rules provide coarse grained operations (configuration management) as well as fine grained operations (in editors, interpreters, and integration tools) Recognize the Information in a Document Image [7] [9] An initial HostGraph is constructed from character recognition and symbol recognition data. The graph edges express geometric relationships among symbols. See Section 5. Graph rewrite rules use geometric relationships to deduce logical relationships, thus constructing a representation of ....

....between arbitrary sets of pattern primitives. Graph rewriting is used to transform the initial, primitive based graph into a final, interpretation based graph. We illustrate this by describing a particular pattern recognition task: the recognition of a mathematical expression from a document image [9]. The code is available on the web [17] A similar style of graph rewriting has been used in the recognition of music notation [7] As shown in Figure 14, a handprinted or typeset mathematical expression is scanned to turn it into an image. Character recognition is applied, resulting in a ....

A. Grbavec and D. Blostein, "Mathematics Recognition Using Graph Rewriting," Third International Conference on Document Analysis and Recognition, Montreal, Canada, August 1995, pp. 417-421.

....it is possible to bypass the symbol recognition step in order to concentrate on symbol arrangement analysis. Test data for the recognition system can be obtained by scanning a mathematical expression, and manually simulating the symbolrecognition step. This approach has been taken in [3] 4] [5] [6] Here, perfect (error free) 4 Handbook on Optical Character Recognition and Document Image Analysis symbol recognition results are used to test the symbol arrangement analysis method. To create a complete recognizer, one must: 1) supply an automatic symbol recognizer, 2) modify the ....

....to g l can be replaced by graph g r . Further information is associated with the graph rewriting rule, to specify how attribute values for g r are computed, and to specify the creation of edges between g r and the main graph. Graph rewriting has been applied to mathematics recognition as follows [5]. The existence of a symbol recognizer is assumed: the input graph contains one node to represent each symbol, with node attributes recording the spatial coordinates of the symbol. Given this initial graph, which contains no edges, graph rewriting rules are applied to add edges representing ....

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A. Grbavec and D. Blostein, Mathematics recognition using graph rewriting, Third Int.Conf. on Document Analysis and Recognition, Montreal, Canada, Aug. 1995, 417--421. Recognition of Mathematical Notation 25

....as on the inherent characteristics of the diagrammatic notation. Keeping these shortcomings in 5 mind, we suggest a few dimensions along which notations could be characterized. We illustrate these ideas with comments based on our work in recognizing music and math notation [FaBl93] Fahm95] [GrBl95]. Subtlety of relative symbol placement. This characteristic of a notation affects how difficult it is to determine logical relationships among symbols from spatial relationships among symbols. In math notation, subtleties in the relative placement of symbols convey critical information. For ....

....The Incorporate phase collapses the information from nodes and edges into the attributes of the remaining nodes. This work is extended to address the uncertainty that may be associated with the identity of the notational primitives [Fahm95] and to perform recognition of mathematical notation [GrBl95]. We plan to investigate the use of graph rewriting in conjunction with a blackboard architecture. If data on the blackboard is stored as a graph, then selected knowledge sources could be coded as graph rewrite rules. ....

A. Grbavec and D. Blostein, "Mathematics Recognition Using Graph Rewriting," Third International Conference on Document Analysis and Recognition, Montreal, Canada, August 1995.

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A. Grbavec and D. Blostein. Mathematics recognition using graph rewriting. In Proc. of ICDAR'95, pages 417-421, 1995.

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GRBAVEC A., BLOSTEIN D., Mathematics Recognition Using Graph Rewriting , in ICDAR'93, France, 1995, pp.417-421.

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A. Grbavec, and D. Blostein, "Mathematics Recognition Using Graph Rewriting", ICDAR'93, France, 1995, pp.417-421.

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