Grouping real functions defined on 3D surfaces

Biasotti, Silvia; Spagnuolo, Michela; Falcidieno, Bianca

doi:10.1016/j.cag.2013.05.007

Cited by 9 publications

(6 citation statements)

References 36 publications

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“…The approach groups the functions in a completely unsupervised manner according to a distance defined on F . The results obtained in [9] show that for a given class of shapes it is possible to identify a (small) number of functions that are mutually independent. For a set F D ff 1 ; : : : ; f n g of n functions defined on a triangle mesh T representing a shape, the distance I .f i ; f j / between two functions f i and f j is given by:…”

Section: Selection Of Representative Functionsmentioning

confidence: 93%

“…In principle, this set of functions is very large; the space of the eigenfunctions of the Laplace-Beltrami operator or heat-kernel functions are possible examples as well as distance-based or geodesic-based functions [9]. We start from a set of 76 functions that in our idea reflects either intrinsic or extrinsic shape features (see [8] for a complete description of these functions), then we cluster them according to the method presented in Sect.…”

Section: Geometric Descriptionmentioning

confidence: 99%

“…In this scenario, we present the clustering approach proposed in [9] to select a subset F 0 Â F of scalar functions that qualitatively define a sort of basis of the shape properties. The approach groups the functions in a completely unsupervised manner according to a distance defined on F .…”

Section: Selection Of Representative Functionsmentioning

confidence: 99%

See 2 more Smart Citations

Shape Analysis and Description Using Real Functions

Biasotti

Cerri

Spagnuolo

et al. 2014

Mathematics and Visualization

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Section: Selection Of Representative Functionsmentioning

confidence: 93%

Section: Geometric Descriptionmentioning

confidence: 99%

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Shape Analysis and Description Using Real Functions

Biasotti

Cerri

Spagnuolo

et al. 2014

Mathematics and Visualization

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“…To select functions, we performed several experiments with different choices of the clustering parameters. Not surprisingly we discovered that the performance of the MDM descriptor increases when discarding approximatively half functions; indeed we are removing redundant and, maybe overfitting, information, see also [BSF13] for more detailed discussions on the selection and grouping of real functions. We used the DBSCAN implementation described in [DWM01], run it on an approximation of the diffusion map obtained with the first three eigenvectors and select t = 3.…”

Section: Geometric Descriptionmentioning

confidence: 99%

PHOG: Photometric and geometric functions for textured shape retrieval

Biasotti

Cerri

Giorgi

et al. 2013

Computer Graphics Forum

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In this paper we target the problem of textured 3D object retrieval. As a first contribution, we show how to include photometric information in the persistence homology setting, also proposing a novel theoretical result about multidimensional persistence spaces. As a second contribution, we introduce a generalization of the integral geodesic distance which fuses shape and color properties. Finally, we adopt a purely geometric description based on the selection of geometric functions that are mutually independent. The photometric, hybrid and geometric descriptions are combined into a signature, whose performance is tested on a benchmark dataset.

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“…The DBSCAN clustering technique for selecting representative geometric functions is replaced by the one used in [8], which is based on the replicator dynamics technique [55]. The modified geometric descriptors are compared via the EMD as well, after converting the M DM matrices into feature vectors.…”

Section: Phog: Photometric and Geometric Functions For Textured Shapementioning

confidence: 99%

Retrieval and classification methods for textured 3D models: a comparative study

et al. 2015

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This paper presents a comparative study of six methods for the retrieval and classification of textured 3D models, which have been selected as representative of the state of the art. To better analyse and control how methods deal with specific classes of geometric and texture deformations, we built a collection of 572 synthetic textured mesh models, in which each class includes multiple texture and geometric modifications of a small set of null models. Results show a challenging, yet lively, scenario and also reveal interesting insights in how to deal with texture information according to different approaches, possibly working in the CIELab as well as in modifications of the RGB colour space.

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Grouping real functions defined on 3D surfaces

Cited by 9 publications

References 36 publications

Shape Analysis and Description Using Real Functions

Shape Analysis and Description Using Real Functions

PHOG: Photometric and geometric functions for textured shape retrieval

Retrieval and classification methods for textured 3D models: a comparative study

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