Abstract: The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.

Abstract: Sketch recognition is a discipline which has gained an increasing interest in the last
20 years. This is due to the appearance of new devices such as PDA, Tablet PC’s
or digital pen & paper protocols. From the wide range of sketched documents we
focus on those that represent structured documents such as: architectural floor-plans,
engineering drawing, UML diagrams, etc. To recognize and understand these kinds
of documents, first we have to recognize the different compounding symbols and then
we have to identify the relations between these elements. From the way that a sketch
is captured, there are two categories: on-line and off-line. On-line input modes refer
to draw directly on a PDA or a Tablet PC’s while off-line input modes refer to scan
a previously drawn sketch.
This thesis is an overlapping of three different areas on Computer Science: Pattern
Recognition, Document Analysis and Human-Computer Interaction. The aim of this
thesis is to interpret sketched documents independently on whether they are captured
on-line or off-line. For this reason, the proposed approach should contain the following
features. First, as we are working with sketches the elements present in our input
contain distortions. Second, as we would work in on-line or off-line input modes, the
order in the input of the primitives is indifferent. Finally, the proposed method should
be applied in real scenarios, its response time must be slow.
To interpret a sketched document we propose a syntactic approach. A syntactic
approach is composed of two correlated components: a grammar and a parser. The
grammar allows describing the different elements on the document as well as their
relations. The parser, given a document checks whether it belongs to the language
generated by the grammar or not. Thus, the grammar should be able to cope with
the distortions appearing on the instances of the elements. Moreover, it would be
necessary to define a symbol independently of the order of their primitives. Concerning to the parser when analyzing 2D sentences, it does not assume an order in the
primitives. Then, at each new primitive in the input, the parser searches among the
previous analyzed symbols candidates to produce a valid reduction.
Taking into account these features, we have proposed a grammar based on Adjacency Grammars. This kind of grammars defines their productions as a multiset
of symbols rather than a list. This allows describing a symbol without an order in
their components. To cope with distortion we have proposed a distortion model.
This distortion model is an attributed estimated over the constraints of the grammar and passed through the productions. This measure gives an idea on how far is the
symbol from its ideal model. In addition to the distortion on the constraints other
distortions appear when working with sketches. These distortions are: overtracing,
overlapping, gaps or spurious strokes. Some grammatical productions have been defined to cope with these errors. Concerning the recognition, we have proposed an
incremental parser with an indexation mechanism. Incremental parsers analyze the
input symbol by symbol given a response to the user when a primitive is analyzed.
This makes incremental parser suitable to work in on-line as well as off-line input
modes. The parser has been adapted with an indexation mechanism based on a spatial division. This indexation mechanism allows setting the primitives in the space
and reducing the search to a neighbourhood.
A third contribution is a grammatical inference algorithm. This method given a
set of symbols captures the production describing it. In the field of formal languages,
different approaches has been proposed but in the graphical domain not so much work
is done in this field. The proposed method is able to capture the production from
a set of symbol although they are drawn in different order. A matching step based
on the Haussdorff distance and the Hungarian method has been proposed to match
the primitives of the different symbols. In addition the proposed approach is able to
capture the variability in the parameters of the constraints.
From the experimental results, we may conclude that we have proposed a robust
approach to describe and recognize sketches. Moreover, the addition of new symbols
to the alphabet is not restricted to an expert. Finally, the proposed approach has
been used in two real scenarios obtaining a good performance.

Abstract: There are printed complex documents where text lines of a single page may have different orientations or the text lines may be curved in shape. As a result, it is difficult to detect the skew of such documents and hence character segmentation and recognition of such documents are a complex task. In this paper, using background and foreground information we propose a novel scheme towards the recognition of Indian complex documents of Bangla and Devnagari script. In Bangla and Devnagari documents usually characters in a word touch and they form cavity regions. To take care of these cavity regions, background information of such documents is used. Convex hull and water reservoir principle have been applied for this purpose. Here, at first, the characters are segmented from the documents using the background information of the text. Next, individual characters are recognized using rotation invariant features obtained from the foreground part of the characters.
For character segmentation, at first, writing mode of a touching component (word) is detected using water reservoir principle based features. Next, depending on writing mode and the reservoir base-region of the touching component, a set of candidate envelope points is then selected from the contour points of the component. Based on these candidate points, the touching component is finally segmented into individual characters. For recognition of multi-sized/multi-oriented characters the features are computed from different angular information obtained from the external and internal contour pixels of the characters. These angular information are computed in such a way that they do not depend on the size and rotation of the characters. Circular and convex hull rings have been used to divide a character into smaller zones to get zone-wise features for higher recognition results. We combine circular and convex hull features to improve the results and these features are fed to support vector machines (SVM) for recognition. From our experiment we obtained recognition results of 99.18% (98.86%) accuracy when tested on 7515 (7874) Devnagari (Bangla) characters.

Abstract: This paper deals with the recognition of symbols and struc- tural textures in architectural plans using string matching techniques. A plan is represented by an attributed graph whose nodes represent characteristic points and whose edges represent segments. Symbols and textures can be seen as a set of regions, i.e. closed loops in the graph, with a particular arrangement. The search for a symbol involves a graph matching between the regions of a model graph and the regions of the graph representing the document. Discriminating a texture means a clus- tering of neighbouring regions of this graph. Both procedures involve a similarity measure between graph regions. A string codification is used to represent the sequence of outlining edges of a region. Thus, the simila- rity between two regions is defined in terms of the string edit distance between their boundary strings. The use of string matching allows the recognition method to work also under presence of distortion.