Shape Decomposition and Shape Similarity Measure

1998 ◽  
pp. 367-376 ◽  
Author(s):  
Longin Jan Latecki ◽  
Rolf Lakämper
Keyword(s):  
Similarity Measure ◽  
Shape Similarity ◽  
Shape Decomposition

scholarly journals POLYHEDRAL MODEL RETRIEVAL USING WEIGHTED POINT SETS

2003 ◽  
Vol 03 (01) ◽  
pp. 209-229 ◽  
Author(s):  
JOHAN W. H. TANGELDER ◽  
REMCO C. VELTKAMP
Keyword(s):  
Similarity Measure ◽  
Triangle Inequality ◽  
Grid Cell ◽  
Shape Similarity ◽  
Salient Point ◽  
Point Sets ◽  
3D Shape ◽  
The Earth ◽  
Weighted Point ◽  
Point Set

Due to the recent improvements in laser scanning technology, 3D visualization and modeling, there is an increasing need for tools supporting the automatic search for 3D objects in archives. In this paper we describe a new geometric approach to 3D shape comparison and retrieval for arbitrary objects described by 3D polyhedral models that may contain gaps. In contrast with the existing approaches, our approach takes the overall relative spatial location into account by representing the 3D shape as a weighted point set. To compare two objects geometrically, we enclose each object by a 3D grid and generate a weighted point set, which represents a salient point for each non-empty grid cell. We compare three methods to obtain a salient point and a weight in each grid cell: (1) choosing the vertex in the cell with the highest Gaussian curvature, and choosing a measure as weight for that curvature, (2) choosing the area-weighted mean of the vertices in the cell, and choosing a measure as weight denoting the normal variation of the facets in the cell and (3) choosing the center of mass of all vertices in the cell, and choosing one as weight. Finally, we compute the similarity between two shapes by comparing their weighted point sets using a new shape similarity measure based on weight transportation that is a variation of the Earth Mover's Distance. Unlike the Earth Mover's Distance, the new shape similarity measure satisfies the triangle inequality. This property makes it suitable for use in indexing schemes, that depend on the triangle inequality, such as the one we introduce, based on the so-called vantage objects. The strength of our approach is proven through experimental results using a database consisting of 133 models such as mugs, cars and boats, and a database consisting of 512 models, mostly air planes, classified into conventional air planes, delta-jets, multi-fuselages, biplanes, helicopters and other models. The results show that the retrieval performance is better than related shape matching methods.

3D Object Classification Based on Volumetric Parts

2011 ◽  
pp. 396-412
Author(s):  
Weiwei Xing ◽  
Weibin Liu ◽  
Baozong Yuan
Keyword(s):  
Similarity Measure ◽  
Object Classification ◽  
Shape Similarity ◽  
Classification Approach ◽  
Partial Matching ◽  
3D Object ◽  
Computation Algorithm ◽  
Model Similarity ◽  
3D Object Classification ◽  
Unknown Object

This article proposes a 3D object classification approach based on volumetric parts, where Superquadricbased Geon (SBG) description is implemented for representing the volumetric constituents of 3D object. In the approach, 3D object classification is decomposed into the constrained search on interpretation tree and the similarity measure computation. First, a set of integrated features and corresponding constraints are presented, which are used for defining efficient interpretation tree search rules and evaluating the model similarity. Then a similarity measure computation algorithm is developed to evaluate the shape similarity of unknown object data and the stored models. By this classification approach, both whole and partial matching results with model shape similarity ranks can be obtained; especially, focus match can be achieved, in which different key parts can be labeled and all the matched models with corresponding key parts can be obtained. Some experiments are carried out to demonstrate the validity and efficiency of the approach for 3D object classification.

scholarly journals Front Shape Similarity Measure for Shape-Oriented Sensitivity Analysis and Data Assimilation for Eikonal Equation

2018 ◽  
Vol 63 ◽  
pp. 258-279 ◽  
Author(s):  
M.C. Rochoux ◽  
A. Collin ◽  
C. Zhang ◽  
A. Trouvé ◽  
D. Lucor ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Data Assimilation ◽  
Similarity Measure ◽  
Eikonal Equation ◽  
Physical Parameters ◽  
Shape Similarity ◽  
Gradient Term ◽  
Near Surface ◽  
Front Shape

We present a shape-oriented data assimilation strategy suitable for front-tracking problems through the example of wildfire. The concept of “front” is used to model, at regional scales, the burning area delimitation that moves, undergoes shape and topological changes under heterogeneous orography, biomass fuel and micrometeorology. The simulation-observation discrepancies are represented using a front shape similarity measure deriving from image processing and based on the Chan-Vese contour fitting functional. We show that consistent corrections of the front location and uncertain physical parameters can be obtained using this measure applied on a level-set fire growth model solving for an eikonal equation. This study involves a Luenberger observer for state estimation, including a topological gradient term to track multiple fronts, and of a reduced-order Kalman filter for joint parameter estimation. We also highlight the need – prior to parameter estimation – for sensitivity analysis based on the same discrepancy measure, and for instance using polynomial chaos metamodels, to ensure a meaningful inverse solution is achieved. The performance of the shape-oriented data assimilation strategy is assessed on a synthetic configuration subject to uncertainties in front initial position, near-surface wind magnitude and direction. The use of a robust front shape similarity measure paves the way toward the direct assimilation of infrared images and is a valuable asset in the perspective of data-driven wildfire modeling.

Robust Multisource Remote Sensing Image Registration Method Based on Scene Shape Similarity

2019 ◽  
Vol 85 (10) ◽  
pp. 725-736 ◽  
Author(s):  
Ming Hao ◽  
Jian Jin ◽  
Mengchao Zhou ◽  
Yi Tian ◽  
Wenzhong Shi
Keyword(s):  
Remote Sensing ◽  
Image Registration ◽  
Similarity Measure ◽  
Template Matching ◽  
Remote Sensing Image ◽  
Shape Similarity ◽  
Remote Sensing Images ◽  
Registration Method ◽  
Sensing Applications ◽  
Global Consistency

Image registration is an indispensable component of remote sensing applications, such as disaster monitoring, change detection, and classification. Grayscale differences and geometric distortions often occur among multisource images due to their different imaging mechanisms, thus making it difficult to acquire feature points and match corresponding points. This article proposes a scene shape similarity feature (SSSF) descriptor based on scene shape features and shape context algorithms. A new similarity measure called SSSFncc is then defined by computing the normalized correlation coefficient of the SSSF descriptors between multisource remote sensing images. Furthermore, the tie points between the reference and the sensed image are extracted via a template matching strategy. A global consistency check method is then used to remove the mismatched tie points. Finally, a piecewise linear transform model is selected to rectify the remote sensing image. The proposed SSSFncc aims to extract the scene shape similarity between multisource images. The accuracy of the proposed SSSFncc is evaluated using five pairs of experimental images from optical, synthetic aperture radar, and map data. Registration results demonstrate that the SSSFncc similarity measure is robust enough for complex nonlinear grayscale differences among multisource remote sensing images. The proposed method achieves more reliable registration outcomes compared with other popular methods.

Shape similarity measure using turn angle cross-correlation for oyster quality evaluation

2010 ◽  
Vol 100 (1) ◽  
pp. 178-186 ◽  
Author(s):  
Guangming Xiong ◽  
Dah-Jye Lee ◽  
Kevin R. Moon ◽  
Robert M. Lane
Keyword(s):  
Similarity Measure ◽  
Cross Correlation ◽  
Quality Evaluation ◽  
Shape Similarity ◽  
Turn Angle

scholarly journals Supporting anthropological research with efficient rotation invariant shape similarity measurement

2006 ◽  
Vol 4 (13) ◽  
pp. 207-222 ◽  
Author(s):  
L Wei ◽  
E Keogh ◽  
X Xi ◽  
S.-H Lee
Keyword(s):  
Similarity Measure ◽  
Distance Measure ◽  
Rotation Invariance ◽  
Longest Common Subsequence ◽  
Distance Measures ◽  
Shape Similarity ◽  
Shape Representations ◽  
Discrimination Ability ◽  
Projectile Points ◽  
Common Subsequence

The matching of two-dimensional shapes is an important problem with many applications in anthropology. Examples of objects that anthropologists are interested in classifying, clustering and indexing based on shape include bone fragments, projectile points (arrowheads/spearpoints), petroglyphs and ceramics. Interest in matching such objects originates from the fundamental question for many biological anthropologists and archaeologists: how can we best quantify differences and similarities? This interest is fuelled in part by a movement that notes: ‘an increasing number of archaeologists are showing interest in employing Darwinian evolutionary theory to explain variation in the material record’. Aiding such research efforts with computers requires a shape similarity measure that is invariant to many distortions, including scale, offset, noise, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However, rotation invariance seems to be uniquely difficult. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of poor discrimination ability, or in the distance measure, at the expense of efficiency. In this work, we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems, our technique can take current approaches and make them four orders of magnitude faster, without false dismissals. Moreover, our technique can be used with any of the dozens of existing shape representations and with all the most popular distance measures, including Euclidean distance, dynamic time warping and longest common subsequence. We show the applications of our work to several important problems in anthropology, including clustering and indexing of skulls, projectile points and petroglyphs.

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