Dietmar Saupe

Feature-based similarity search in 3D object databases

The development of effective content-based multimedia search systems is an important research issue due to the growing amount of digital audio-visual information. In the case of images and video, the growth of digital data has been observed since the introduction of 2D capture devices. A similar development is expected for 3D data as acquisition and dissemination technology of 3D models is constantly improving. 3D objects are becoming an important type of multimedia data with many promising application possibilities. Defining the aspects that constitute the similarity among 3D objects and designing algorithms that implement such similarity definitions is a difficult problem. Over the last few years, a strong interest in methods for 3D similarity search has arisen, and a growing number of competing algorithms for content-based retrieval of 3D objects have been proposed. We survey feature-based methods for 3D retrieval, and we propose a taxonomy for these methods. We also present experimental results, comparing the effectiveness of some of the surveyed methods.

Tools for 3D-object retrieval: Karhunen-Loeve transform and spherical harmonics

We present tools for 3D object retrieval in which a model, a polygonal mesh, serves as a query and similar objects are retrieved from a collection of 3D objects. Algorithms proceed first by a normalization step (pose estimation) in which models are transformed into a canonical coordinate frame. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. Using a metric in the feature vector space nearest neighbors are computed and ranked. Objects thus retrieved are displayed for inspection, selection, and processing. For the pose estimation we introduce a modified Karhunen-Loeve transform that takes into account not only vertices or polygon centroids from the 3D models but all points in the polygons of the objects. Some feature vectors can be regarded as samples of functions on the 2-sphere. We use Fourier expansions of these functions as uniform representations allowing embedded multi-resolution feature vectors. Our implementation demonstrates and visualizes these tools.

3D Model Retrieval with Spherical Harmonics and Moments

We consider 3D object retrieval in which a polygonal mesh serves as a queryand similar objects are retrieved from a collection of 3D objects. Algorithms proceed first bya normalization step in which models are transformed into canonical coordinates. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. In the feature vector space nearest neighbors are computed and ranked. Retrieved objects are displayed for inspection, selection, and processing. Our feature vectors are based on rays cast from the center of mass of the object. For each raythe object extent in the raydirection yields a sample of a function on the sphere. We compared two kinds of representations of this function, namelyspherical harmonics and moments. Our empirical comparison using precision-recall diagrams for retrieval results in a data base of 3D models showed that the method using spherical harmonics performed better.

Fractals for the Classroom

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Description of 3D-shape using a complex function on the sphere

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Accelerating fractal image compression by multi-dimensional nearest neighbor search

We propose a novel feature vector suitable for searching collections of 3D-object images by shape similarity. In this search, a polygonal mesh model serves as a query. For each model, feature vectors are automatically extracted and stored. Shape similarity between 3D-objects in the search space is determined by finding and ranking nearest neighbors in the feature vector space. Ranked objects are retrieved for inspection, selection, and processing. The feature vector is obtained by forming a complex function on the sphere. Afterwards, we apply the fast Fourier transform (FFT) on the sphere and obtain Fourier coefficients for spherical harmonics. The absolute values of the coefficients form the feature vector. Retrieval efficiency of the new approach is evaluated by constructing precision/recall diagrams and using two different 3D-model databases. We compared the approach with two methods based on real functions on the sphere. Our empirical comparison showed that the complex feature vector performed best. We also prepared a Web-based retrieval system for testing the methods discussed.

Spectral-Driven Isometry-Invariant Matching of 3D Shapes

In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find the best match for another image portion. Our theory developed here shows that this basic procedure of fractal image compression is equivalent to multi-dimensional nearest neighbor search. This result is useful for accelerating the encoding procedure in fractal image compression. The traditional sequential search takes linear time whereas the nearest neighbor search can be organized to require only logarithmic time. The fast search has been integrated into an existing state-of-the-art classification method thereby accelerating the searches carried out in the individual domain classes. In this case we record acceleration factors from 1.3 up to 11.5 depending on image and domain pool size with negligible or minor degradation in both image quality and compression ratio. Furthermore, as compared to plain classification our method is demonstrated to be able to search through larger portions of the domain pool without increased the computation time.

Fast algorithm for rate-based optimal error protection of embedded codes

This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on point-based statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eigenvalues of the Laplace-Beltrami operator. These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density and number of reference points. Once a set of reference points has been computed, for each of them we construct a point-based statistical descriptor (PSSD, for short) of the input surface. This descriptor incorporates an approximation of the geodesic shape distribution and other geometric information describing the surface at that point. Then, the dissimilarity between two surfaces is computed by comparing the corresponding sets of PSSDs with bipartite graph matching or measuring the L1-distance between the reordered feature vectors of a proximity graph. Here, the reordering is given by the Fiedler vector of a Laplacian matrix associated to the proximity graph. Our tests have shown that both approaches are suitable for online retrieval of deformed objects and our sampling strategy improves the retrieval performances of isometry-invariant matching methods. Finally, the approach based on the Fiedler vector is faster than using the bipartite graph matching and it has a similar retrieval effectiveness.

An experimental effectiveness comparison of methods for 3D similarity search

Embedded image codes are very sensitive to channel noise because a single bit error can lead to an irreversible loss of synchronization between the encoder and the decoder. P.G. Sherwood and K. Zeger (see IEEE Signal Processing Lett., vol.4, p.191-8, 1997) introduced a powerful system that protects an embedded wavelet image code with a concatenation of a cyclic redundancy check coder for error detection and a rate-compatible punctured convolutional coder for error correction. For such systems, V. Chande and N. Farvardin (see IEEE J. Select. Areas Commun., vol.18, p.850-60, 2000) proposed an unequal error protection strategy that maximizes the expected number of correctly received source bits subject to a target transmission rate. Noting that an optimal strategy protects successive source blocks with the same channel code, we give an algorithm that accelerates the computation of the optimal strategy of Chande and Farvardin by finding an explicit formula for the number of occurrences of the same channel code. Experimental results with two competitive channel coders and a binary symmetric channel showed that the speed-up factor over the approach of Chande and Farvardin ranged from 2.82 to 44.76 for transmission rates between 0.25 and 2 bits per pixel.

Automatic selection and combination of descriptors for effective 3D similarity search

Methods for content-based similarity search are fundamental for managing large multimedia repositories, as they make it possible to conduct queries for similar content, and to organize the repositories into classes of similar objects. 3D objects are an important type of multimedia data with many promising application possibilities. Defining the aspects that constitute the similarity among 3D objects, and designing algorithms that implement such similarity definitions is a difficult problem. Over the last few years, a strong interest in 3D similarity search has arisen, and a growing number of competing algorithms for the retrieval of 3D objects have been proposed. The contributions of this paper are to survey a body of recently proposed methods for 3D similarity search, to organize them along a descriptor extraction process model, and to present an extensive experimental effectiveness and efficiency evaluation of these methods, using several 3D databases.