Elsevier

Pattern Recognition

Volume 39, Issue 7, July 2006, Pages 1380-1390
Pattern Recognition

Detection of a polymorphic Mesoamerican symbol using a rule-based approach

https://doi.org/10.1016/j.patcog.2005.11.019Get rights and content

Abstract

This paper describes a technique to recognize a Mesoamerican symbol whose shape is extremely variable. We extract symbols from a drawing and we encode them as discrete curves. We perform the recognition using a set of rules that define the correct symbol. One of the rules is the presence of a single symmetry axis. We describe a comparison metric between curves in order to search for symmetries. The other rules used for the recognition concern the morphology of the symbol. The proposed technique proves to be fast and efficient. We present recognition results obtained on various pre-hispanic images. The rule-based approach proposed and implemented here, appears suitable to detect polymorphic signs, a common feature of Mesoamerican symbols. To the best of our knowledge, this is the first study of pattern recognition into the field of Mesoamerican iconography.

Introduction

Most of the high cultures developed in Mesoamerica (Olmec, Maya, Teotihuacan, Aztec, etc.), characteristically used plastic shapes and media to represent religious thinking. Those images are then, direct sources of data on the subject and have been studied by iconography and other disciplines, in pursuing that fundamental piece of knowledge. The vastness and complexity of such a universe, however, have naturally limited research to specific sites, cultures, regions and epochs. Even so, few studies have conceived the Mesoamerican iconographic complex as a whole, focusing on the common elements found in different cultures, times and regions [1], [2], [3], [4]. With the same approach and comparative iconographic analyzes, four main signs have been recently identified in a large sample of Mesoamerican monuments [5], [6]. Based on their high incidence in different cultures, regions and epochs in Mesoamerica, their continuous presence in principal monuments, and the central positions they often occupied in images, they have been identified as symbols.

In this work, the polymorphic shape of one of those symbols was studied, defined and compared by pattern recognition means. Thus, this work deals with shape of symbols. Shape is an intrinsic property of objects. Whereas color, motion, and intensity are relatively simply quantified by a few well-understood parameters, shape is much more subtle [7]. Natural or painted shapes are incredibly complex. It is not clear what aspects of shapes are important for applications such as recognition. Several authors have used different techniques for shape analysis and recognition, such as sequential extraction of shape features [8], medial axis transforms, mirroring axes [9]. Pavlidis [10] reviewed these and other methods.

Ballard and Brown [7] proposed the template matching, which is an operation for finding out how well a template (a shape) matches a window of a given binary image. This binary image may be considered as another shape. Strachan et al. [11] presented a method to compare the shapes of two fishes based on invariant moments, optimization of the mismatch, and shape descriptors. Another measure of shape similarity was presented in Ref. [12] by means of the shape numbers, which are related to the resolution of the digitalization scheme. These methods find the best matching between shapes.

Recently, other methods related to shape similarity have been proposed. Gunsel and Tekalp [13] propose a new shape-similarity metric in two eigenshape space for object/image retrieval from a visual database via query-by-example. Carlin [14] presents five different new performance measures for shape similarity retrieval. Mokhtarian and Abbasi [15] propose a method for shape-similarity retrieval under affine transforms based on the maxima of curvature scale space image. Mahmoudi et al. [16] present a method for image retrieval based on shape similarity by edge orientation autocorrelogram. Torsello and Hancock [17] propose a skeletal measure of 2D shape similarity.

Due to the complexity to detect Mesoamerican symbols, which are polymorphic, we propose a rule-based approach. Several authors have used this type of approach, such as: Ding and Young [18] have implemented a rule-based system to complete shape from imperfect contour. Another example of this type of systems is presented by Ahmed and Ward [19], who developed a novel rule-based system for thinning of characters. In this paper, we define a few rules that appear to be common to the many forms of the studied symbol. These rules are general enough to characterize the symbol in spite of its variability but they are specific enough to discriminate between correct and incorrect symbols in most of the cases. In Section 2, we will present an overview of the problem we want to solve and the approach we developed. In Section 3, we will describe the preliminary stages of extracting shapes from an image and normalizing them. In Sections 4 and 5, we will explain in more details the implementation of the proposed rules, concerning the number of symmetry axes and the morphology of the shape, respectively. In Section 6, we will give some recognition results. We will present our conclusions in Section 7.

Section snippets

Presentation of the problem and proposed solution

Iconographists have constituted large databases of pictures and drawings of Mesoamerican artifacts and monuments. We would like to be able to perform an unsupervised inspection of this database and automatically locate in each image some particular symbols. The symbol we study in this paper is the most basic of four newly identified transcultural Mesoamerican signs [5], [6]. We refer to it as the symbol One. Fig. 1 shows a few examples of occurrences of this symbol. It can be seen that there is

Shape extraction

Segmenting an image to extract symbols is by itself a difficult problem that exceeds the limits of this paper. In order to simplify the problem, we assume that our input image is a binary (black and white) line drawing. We also assume that the image is clean: contours are not erroneously interrupted and there are no extraneous connections due to noise. Such an image can be a hand drawing or the result of a filtered edge detection on a more complex image. The proposed technique works as well on

Number of symmetry axes

The idea we use in order to determine whether a symbol is symmetric with respect to a particular axis, is to measure the similarity between the original loop and its mirror image with respect to the considered axis. We therefore need to define a way to compare two curves.

Morphology analysis

The presence of a unique symmetry axis is a necessary but insufficient property to recognize a One. The other prominent characteristics of a One is its arch shape. Since the symbols we study are usually not perfectly symmetric, we separately analyze the shape of both halves of each loop. In order to help this analysis, we first modify the coding of the symbols as described below.

Results

We now apply the proposed technique on several test images. The first attempt is done on the image of Fig. 1 that contains many different examples of Ones. All of them are correctly recognized. Fig. 10 shows other instances of Ones with additional ornaments. We drew in black the parts of the image that are recognized as Ones and in light gray the rejected parts. It can be seen that the Ones are correctly extracted and recognized. In Fig. 11, symbols S1 through S3 are correctly recognized as

Conclusions

In this paper, we have presented a technique to recognize a Mesoamerican symbol that has a very variable shape. In order to deal with this variability, we have proposed an approach based on a series of rules that are common to all the instances of the symbol. The rules we have used are one of symmetry and a few rules of morphology. The number of rules is actually very small and simple enough so that the processing time of a complete image—including extraction of the symbols—is quite small

Acknowledgements

The authors’ gratitude is extended to Professor Rubén Bonifaz Nuño for his continuous support and encouragement in this work. In addition, the authors wish to thank Dr. Hermilo Sanchez Cruz and Lic. Yazmin Ocadiz Martinez for their useful scientific discussions. This study was supported in part by CONACYT, Mexico, Grant C-811-2000.

About the Author—YANN FRAUEL obtained the M.Sc. degree in Optics in 1995 and the Ph.D. degree in Photonics in 1999, both from the Institut d’Optique—Université Paris XI (France). He carried out two postdoctoral stays, respectively, at the University of Cambridge (UK) and at the University of Connecticut (USA). Since 2002, he has been an Associate Researcher with the Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas of the Universidad Nacional Autónoma de México (Mexico). His

References (26)

  • E. Belogay et al.

    Calculating the Hausdorff distance between curves

    Inform. Process. Lett.

    (1997)
  • M. Covarrubias

    Indian Art of Mexico and Central America

    (1957)
  • R. Bonifaz Nuño

    Imagen de Tláloc: Hipótesis iconográfica y textual

    (1986)
  • Cited by (9)

    • Mirror symmetry detection in curves represented by means of the Slope Chain Code

      2019, Pattern Recognition
      Citation Excerpt :

      Frauel et. al. presented in [32] a method to automatically locate symbol One in different mesoamerican drawings. Their method to determine if a symbol is mirror symmetric consisted in using a variation of the Frétchet distance, measuring the similarity of half the contour against its mirror image, with respect to the considered axis.

    • Bag of k-nearest visual words for hieroglyph retrieval

      2019, Journal of Intelligent and Fuzzy Systems
    • Design and test of unmanned aerial vehicle video transfer system based on WiFi

      2015, Nongye Gongcheng Xuebao/Transactions of the Chinese Society of Agricultural Engineering
    • Automatic egyptian hieroglyph recognition by retrieving images as texts

      2013, MM 2013 - Proceedings of the 2013 ACM Multimedia Conference
    View all citing articles on Scopus

    About the Author—YANN FRAUEL obtained the M.Sc. degree in Optics in 1995 and the Ph.D. degree in Photonics in 1999, both from the Institut d’Optique—Université Paris XI (France). He carried out two postdoctoral stays, respectively, at the University of Cambridge (UK) and at the University of Connecticut (USA). Since 2002, he has been an Associate Researcher with the Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas of the Universidad Nacional Autónoma de México (Mexico). His current research interests are in the domains of 3D acquisition techniques and pattern recognition.

    About the Author—OCTAVIO QUESADA obtained the B.Sc. degree in Basic Biomedical Research in 1986, and the Ph.D. in Neurochemistry in 1990, from the Universidad Nacional Autónoma de México (UNAM). He has worked as full time researcher at the Neurosciences Department of the Instituto de Fisiología Celular, UNAM, for 10 years. Since April of 2000, he is ascribed to the Instituto de Investigaciones Filológicas of the same university, were he develops studies on Mesoamerican iconography.

    About the Author—ERNESTO BRIBIESCA received the B.Sc. degree in electronics engineering from the Instituto Politécnico Nacional in 1976. He received the Ph.D. degree in Mathematics from the Universidad Autónoma Metropolitana (UAM) in 1996, he was researcher at the IBM Latin American Scientific Center, and at the Dirección General de Estudios del Territorio Nacional (DETENAL). He is associate editor of the Pattern Recognition journal. He has twice been chosen Honorable Mention winner of the Annual Pattern Recognition Society Award. Currently, he is Professor at the Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS) at the Universidad Nacional Autónoma de México (UNAM), where he teaches graduate courses in Pattern Recognition.

    View full text