scholarly journals Class Representation of Shapes Using Qualitative-codes

10.14311/224 ◽  
2001 ◽  
Vol 41 (3) ◽  
Author(s):  
Ashraf Fouad Hafez Ismail
Keyword(s):  
Coding Theory ◽  
Geometric Modeling ◽  
Shape Representation ◽  
Simple Task ◽  
Shape Information ◽  
Shape Comparison ◽  
Qualitative Shape ◽  
Shape Descriptions ◽  
Cartesian Coordinate ◽  
Class Representation

This paper introduces our qualitative shape representation formalism that is devised to overcome, as we have argued, the class abstraction problems created by numeric schemes. The numeric shape representation method used in conventional geometric modeling systems reveals difficulties in several aspects of architectural designing. Firstly, numeric schemes strongly require complete and detailed information for any simple task of object modeling. This requirement of information completeness makes it hard to apply numeric schemes to shapes in sketch level drawings that are characteristically ambiguous and have non-specific limitations on shape descriptions. Secondly, Cartesian coordinate-based quantitative shape representation schemes show restrictions in the task of shape comparison and classification that are inevitably involved in abstract concepts related to shape characteristics. One of the reasons why quantitative schemes are difficult to apply to the abstraction of individual shape information into its classes and categories is the uniqueness property, meaning that an individual description in a quantitative scheme should refer to only one object in the domain of representation. A class representation, however, should be able to indicate not only one but also a group of objects sharing common characteristics. Thirdly, it is difficult or inefficient to apply numeric shape representation schemes based on the Cartesian coordinate system to preliminary shape analysis and modeling tasks because of their emphasis on issues, such as detail, completeness, uniqueness and individuality, which can only be accessed in the final stages of designing. Therefore, we face the need for alternative shape representation schemes that can handle class representation of objects in order to manage the shapes in the early stages of designing. We consider shape as a boundary description consisting of a set of connected and closed lines. Moreover, we need to consider non-numeric approaches to overcome the problems caused by quantitative representation approaches.This paper introduces a qualitative approach to shape representation that is contrasted to conventional numeric techniques. This research is motivated by ideas and methodologies from related studies such as in qualitative formalism ([4], [6], [19], [13], [31]), qualitative abstraction [16], qualitative vector algebra ([7], [32]), qualitative shapes ([18], [23], [21]), and coding theory ([20], [25], [26], [1], [2], [3], [22]). We develop a qualitative shape representation scheme by adopting propitious aspects of the above techniques to suit the need for our shape comparison and analysis tasks. The qualitative shape-encoding scheme converts shapes into systematically constructed qualitative symbols called Q-codes. This paper explains how the Q-code scheme is developed and applied.

A Point-Structured Geometric Modeling Approach to Foot Shape Representation

2012 ◽  
Author(s):  
Ming J. Tsai ◽  
Hung W. Lee ◽  
Hsueh Y. Lung
Keyword(s):  
Geometric Modeling ◽  
Shape Representation ◽  
Geometric Model ◽  
Quantitative Description ◽  
Compact Representation ◽  
Shape Information ◽  
Modeling Approach ◽  
Data Points ◽  
3D Geometric Model ◽  
Structured Representation

A compact representation for the quantitative description of foot shape is important not only for the foot measurement and anthropometry, but also for the ergonomic design of footwear. Based on foot scanned data, a novel point-structured geometric modeling approach to the reduction of 3D point cloud and the preservation of shape information is proposed. The semantic descriptions of foot features are interpreted into logical definitions. A total of fifteen feature points are thus defined. Finally, there are only a total of 2,093 data points needed in such a point-structured representation. Based on it, it is easy to fetch not only the 1D and 2D measurements, but also the 3D feature curves of the foot shape. It can provide a compact 3D geometric model to serve as a significant database for the individuals and, thereby, becomes a useful tool in investigating the foot and manufacturing the foot related apparel and devices.

scholarly journals Representation and recognition of the spatial organization of three-dimensional shapes

1978 ◽  
Vol 200 (1140) ◽  
pp. 269-294 ◽  
Keyword(s):  
Coordinate System ◽  
Spatial Organization ◽  
Shape Representation ◽  
Shape Recognition ◽  
Three Dimensional ◽  
Modular Organization ◽  
Shape Description ◽  
Shape Information ◽  
Constraint Analysis ◽  
Shape Descriptions

The human visual process can be studied by examining the computational problems associated with deriving useful information from retinal images. In this paper, we apply this approach to the problem of representing three-dimensional shapes for the purpose of recognition. 1. Three criteria, accessibility, scope and uniqueness , and stability and sensitivity , are presented for judging the usefulness of a representation for shape recognition. 2. Three aspects of a representation’s design are considered, (i) the representation’s coordinate system, (ii) its primitives, which are the primary units of shape information used in the representation, and (iii) the organization the representation imposes on the information in its descriptions. 3. In terms of these design issues and the criteria presented, a shape representation for recognition should: (i) use an object-centred coordinate system, (ii) include volumetric primitives of varied sizes, and (iii) have a modular organization. A representation based on a shape’s natural axes (for example the axes identified by a stick figure) follows directly from these choices. 4. The basic process for deriving a shape description in this representation must involve: (i) a means for identifying the natural axes of a shape in its image and (ii) a mechanism for transforming viewer-centred axis specifications to specifications in an object-centred coordinate system. 5. Shape recognition involves: (i) a collection of stored shape descriptions, and (ii) various indexes into the collection that allow a newly derived description to be associated with an appropriate stored description. The most important of these indexes allows shape recognition to proceed conservatively from the general to the specific based on the specificity of the information available from the image. 6. New constraints supplied by a conservative recognition process can be used to extract more information from the image. A relaxation process for carrying out this constraint analysis is described.

Shape Similarity Matching With Octree Representations

2006 ◽  
Author(s):  
Jingsheng Zhang ◽  
Shana Smith
Keyword(s):  
Shape Matching ◽  
Shape Representation ◽  
Data Retrieval ◽  
Data File ◽  
The Internet ◽  
Shape Information ◽  
Shape Representations ◽  
3D Shape ◽  
Space Efficiency ◽  
Octree Representation

Shape matching is one of the fundamental problems in content-based 3D shape retrieval. Since there are typically a large number of possible matches in a shape database, there is a crucial need to perform shape matching efficiently. As a result, shapes must be reduced into a simpler shape representation, and computational complexity is one of the most important criteria for evaluating 3D shape representations. To meet the need, the investigators have implemented a new effective and efficient approach for 3D shape matching, which uses a simplified octree representation of 3D mesh models. The simplified octree representation was developed to improve time and space efficiency over prior representations. In addition, octree representations are rapidly becoming the standard file format for delivering 3D content across the Internet. The proposed approach stores octree information in XML files, rather than using a new data file type, to facilitate comparing models over the Internet. New methods for normalizing models, generating octrees, and comparing models were developed. The proposed approach allows users to efficiently exchange shape information and compare models over the Internet, in standardized data and data file formats, without transferring exact model files. The proposed approach is the first step in a project which will build a complete 3D model database and data retrieval system, which can be incorporated with other data mining techniques.

scholarly journals Learning Shape Representations for Multi-Atlas Endocardium Segmentation in 3D Echo Images

2014 ◽  
Author(s):  
Ozan Oktay ◽  
Wenzhe Shi ◽  
Kevin Keraudren ◽  
Jose Caballero ◽  
Daniel Rueckert
Keyword(s):  
State Of The Art ◽  
Shape Representation ◽  
Speckle Reduction ◽  
Reduction Step ◽  
Shape Information ◽  
Shape Representations ◽  
Segmentation Framework ◽  
Echocardiographic Images ◽  
Atlas Segmentation ◽  
First Time

As part of the CETUS challenge, we present a multi-atlas segmentation framework to delineate the left-ventricle endocardium in echocardiographic images. To increase the robustness of the registration step, we introduce a speckle reduction step and a new shape representation based on sparse coding and manifold approximation in dictionary space. The shape representation, unlike intensity values, provides consistent shape information across different images. The validation results on the test set show that registration based on our shape representation significantly improves the performance of multi-atlas segmentation compared to intensity based registration. To our knowledge it is the first time that multi-atlas segmentation achieves state-of-the-art results for echocardiographic images.

scholarly journals Measures of Similarity Between Objects Based on Qualitative Shape Descriptions

2013 ◽  
Vol 13 (3) ◽  
pp. 181-218 ◽  
Author(s):  
Zoe Falomir ◽  
Luis Gonzalez-Abril ◽  
Lledó Museros ◽  
Juan Antonio Ortega
Keyword(s):  
Qualitative Shape ◽  
Shape Descriptions

scholarly journals Strategies of shape representation in macaque visual area V2

2003 ◽  
Vol 20 (3) ◽  
pp. 313-328 ◽  
Author(s):  
JAY HEGDÉ ◽  
DAVID C. VAN ESSEN
Keyword(s):  
Image Segmentation ◽  
Principal Components ◽  
Visual Cues ◽  
Shape Representation ◽  
Strong Correlations ◽  
Shape Information ◽  
Object Shape ◽  
Surface Textures ◽  
Area V2 ◽  
Response Variation

Contours and surface textures provide powerful cues used in image segmentation and the analysis of object shape. To learn more about how the visual system extracts and represents these visual cues, we studied the responses of V2 neurons in awake, fixating monkeys to complex contour stimuli (angles, intersections, arcs, and circles) and texture patterns such as non-Cartesian gratings, along with conventional bars and sinusoidal gratings. Substantial proportions of V2 cells conveyed information about many contour and texture characteristics associated with our stimuli, including shape, size, orientation, and spatial frequency. However, the cells differed considerably in terms of their degree of selectivity for the various stimulus characteristics. On average, V2 cells responded better to grating stimuli but were more selective for contour stimuli. Metric multidimensional scaling and principal components analysis showed that, as a population, V2 cells show strong correlations in how they respond to different stimulus types. The first two and five principal components accounted for 69% and 85% of the overall response variation, respectively, suggesting that the response correlations simplified the population representation of shape information with relatively little loss of information. Moreover, smaller random subsets of the population carried response correlation patterns very similar to the population as a whole, indicating that the response correlations were a widespread property of V2 cells. Thus, V2 cells extract information about a number of higher order shape cues related to contours and surface textures and about similarities among many of these shape cues. This may reflect an efficient strategy of representing cues for image segmentation and object shape using finite neuronal resources.

scholarly journals Constant curvature modeling of abstract shape representation

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0254719
Author(s):  
Nicholas Baker ◽  
Philip J. Kellman
Keyword(s):  
Visual System ◽  
Constant Curvature ◽  
Shape Representation ◽  
Recognition Task ◽  
Human Perception ◽  
Human Visual Perception ◽  
Abstract Shape ◽  
Perceptual Performance ◽  
Parameterized Model ◽  
Shape Descriptions

How abstract shape is perceived and represented poses crucial unsolved problems in human perception and cognition. Recent findings suggest that the visual system may encode contours as sets of connected constant curvature segments. Here we describe a model for how the visual system might recode a set of boundary points into a constant curvature representation. The model includes two free parameters that relate to the degree to which the visual system encodes shapes with high fidelity vs. the importance of simplicity in shape representations. We conducted two experiments to estimate these parameters empirically. Experiment 1 tested the limits of observers’ ability to discriminate a contour made up of two constant curvature segments from one made up of a single constant curvature segment. Experiment 2 tested observers’ ability to discriminate contours generated from cubic splines (which, mathematically, have no constant curvature segments) from constant curvature approximations of the contours, generated at various levels of precision. Results indicated a clear transition point at which discrimination becomes possible. The results were used to fix the two parameters in our model. In Experiment 3, we tested whether outputs from our parameterized model were predictive of perceptual performance in a shape recognition task. We generated shape pairs that had matched physical similarity but differed in representational similarity (i.e., the number of segments needed to describe the shapes) as assessed by our model. We found that pairs of shapes that were more representationally dissimilar were also easier to discriminate in a forced choice, same/different task. The results of these studies provide evidence for constant curvature shape representation in human visual perception and provide a testable model for how abstract shape descriptions might be encoded.

scholarly journals A graph-based method for fitting planar B-spline curves with intersections

2015 ◽  
Vol 3 (1) ◽  
pp. 14-23 ◽  
Author(s):  
Pengbo Bo ◽  
Gongning Luo ◽  
Kuanquan Wang
Keyword(s):  
Shape Representation ◽  
Line Drawing ◽  
Weighted Graph ◽  
Point Clouds ◽  
Connected Components ◽  
Shape Information ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Shape Characteristics

Abstract The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

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