Combinatorial analysis of ramified patterns and computer imagery of trees

Eyrolles, G.; Janey, Nicolas; Arquès, Didier

doi:10.1145/74333.74336

Cited by 43 publications

(34 citation statements)

References 26 publications

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“…MacDonald [94, pages 110-121] surveys this and other methods applicable to biological and geographical data such as stream networks. Of special interest are methods proposed by Horton [70,71] and Strahler, which served as a basis for synthesizing botanical trees [37,152] (Figure 1.21). …”

Section: Axial Treesmentioning

confidence: 99%

The Algorithmic Beauty of Plants

Prusinkiewicz

Lindenmayer²

1990

The Virtual Laboratory

1,886

1,209

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With 150 Illustrations, 48 in ColorThis edition of The Alogirthmic Beauty of Plants is the electronic version of the book that was published by Springer-Verlag, New York, in 1990 and reprinted in 1996. The electronic version has been produced using the original L A T E X files and digital illustrations. Front cover design: The roses in the foreground (Roses by D. R. Fowler, J. Hanan and P. ) were modeled using L-systems. Distributed ray-tracing with one extended light source was used to simulate depth of field. The roses were placed on a background image (photgraphy by G. Rossbach), which was scanned digitally and post-processed. PrefaceThe beauty of plants has attracted the attention of mathematicians for Mathematics and beauty centuries. Conspicuous geometric features such as the bilateral symmetry of leaves, the rotational symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most extensively. This focus is reflected in a quotation from Weyl [159, page 3], "Beauty is bound up with symmetry."This book explores two other factors that organize plant structures and therefore contribute to their beauty. The first is the elegance and relative simplicity of developmental algorithms, that is, the rules which describe plant development in time. The second is self-similarity, characterized by Mandelbrot [95, page 34] as follows:When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar.This corresponds with the biological phenomenon described by Herman, Lindenmayer and Rozenberg [61]:In many growth processes of living organisms, especially of plants, regularly repeated appearances of certain multicellular structures are readily noticeable.... In the case of a compound leaf, for instance, some of the lobes (or leaflets), which are parts of a leaf at an advanced stage, have the same shape as the whole leaf has at an earlier stage.Thus, self-similarity in plants is a result of developmental processes.Growth and form By emphasizing the relationship between growth and form, this book follows a long tradition in biology. D'Arcy Thompson [143] traces its origins to the late seventeenth century, and comments:Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space. This concept is echoed by Hallé, Oldeman and Tomlinson [58]:The idea of the form implicitly contains also the history of such a form. vi PrefaceThe developmental processes are captured using the formalism of L-systems. They were introduced in 1968 by Lindenmayer [82] as a Modeling of plants theoretical framework for studying the development of simple multicellular organisms, and subsequently applied to investigate higher plants and plant organs. After the incorporation of geometric features, plant models expressed using L-systems became detailed enough to allow the use of computer graphics for realistic visualization of p...

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Section: Axial Treesmentioning

confidence: 99%

The Algorithmic Beauty of Plants

Prusinkiewicz

Lindenmayer²

1990

The Virtual Laboratory

1,886

1,209

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“…The lateral branching is identified by labels j≠k, while j=k identifies bifurcation into child branches of the same order. The method for R matrix estimation from ductal trees has been described previously [7]. The R matrices estimated from clinical images have been used to realistically generate synthetic ductal network [8].…”

Section: Description Of Ductal Topologymentioning

confidence: 99%

Comparison of Methods for Classification of Breast Ductal Branching Patterns

Bakić

Kontos

Megalooikonomou

et al. 2006

Digital Mammography

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Abstract. Topological properties of the breast ductal network have shown the potential for classifying clinical breast images with and without radiological findings. In this paper, we review three methods for the description and classification of breast ductal topology. The methods are based on ramification matrices and symbolic representation employing text mining techniques.. The performance of these methods has been compared using clinical x-ray and MR images of breast ductal networks. We observed the accuracy of the classification between the ductal trees segmented from the x-ray galactograms with radiological findings and normal cases in the range of 0.86-0.91%. The accuracy of the classification of the ductal trees segmented from the MR autogalactograms was observed in the range of 0.5-0.89%.

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“…More realistic model of ductal network may be achieved by various tree modeling algorithms [15]- [17]. Typically, they approach modeling at two levels: (i) topological, where a topological tree, underlying the real one, is constructed, and (ii) geometrical, where the individual tree elements, branches and leaves, are designed in order to capture the shape of the real tree as close as possible.…”

Section: Modeling Ductal Networkmentioning

confidence: 99%

“…Focus of most algorithms is on capturing rules of tree development, used in recursive modeling of tree shape [15], [16]. An approach based on the ramification matrices [17], on the other hand, focuses more on description and control of the final shape, while still on the topological level. Ramification matrices describe branching pattern of a tree and allow classification between different groups of tree structures (e.g., the basic ones: perfect tree, random binary tree, self similar fern, etc.)…”

Section: Modeling Ductal Networkmentioning

confidence: 99%

“…Due to the small number of analyzed ductograms we decided to use the ramification matrix corresponding to the random binary tree rather then the inferred one. Intuitively, random binary tree seems to be the most natural choice out of the structures analyzed in the literature [17] ideal binary tree, random binary tree, self-similar fern.…”

Section: Modeling Ductal Networkmentioning

confidence: 99%

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Mammogram Screening by Automated Followup: A Feasibility Study

Brzakovic¹

1999

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington. VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. AGENCY USE ONLY (Leave blank)REPORT DATE July 1999 REPORT TYPF ANn DATFS HnVFRFDAnnual ( ABSTRACT (Maximum 200 words)This report describes part of a study aimed at developing a computer-based aid for mammogram screening that makes a detailed comparison between mammograms of the same patient acquired at different screenings and detects changes indicative of cancer. The focus of the work in the past three years has been on putting two mammograms acquired at different time into correspondence. The essence of the approach is identification of control points in two mammograms; these points are used to put regions in two mammograms into correspondence. The emphasis of the work in the past year has been on improving the procedure for determining control points, i.e., points that are the same in two images. For this purpose we have developed a model based approach to identify regions of interest in two mammograms. The model encompasses breast tissue characteristics, modeling of compression effects and formation of Xray images. The model is utilized to develop appropriate segmentation operators and the report discusses utilization of the model to detect lobules and ducts. The model can also be utilized for generating synthetic mammograms.Presently, we are evaluating the improvements this approach offers, relative to our original approach, in terms of determining more reliably control points, namely branching points of ducts.

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Combinatorial analysis of ramified patterns and computer imagery of trees

Cited by 43 publications

References 26 publications

The Algorithmic Beauty of Plants

The Algorithmic Beauty of Plants

Comparison of Methods for Classification of Breast Ductal Branching Patterns

Mammogram Screening by Automated Followup: A Feasibility Study

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