Michael Clausen

Efficient content-based retrieval of motion capture data

The reuse of human motion capture data to create new, realistic motions by applying morphing and blending techniques has become an important issue in computer animation. This requires the identification and extraction of logically related motions scattered within some data set. Such content-based retrieval of motion capture data, which is the topic of this paper, constitutes a difficult and time-consuming problem due to significant spatio-temporal variations between logically related motions. In our approach, we introduce various kinds of qualitative features describing geometric relations between specified body points of a pose and show how these features induce a time segmentation of motion capture data streams. By incorporating spatio-temporal invariance into the geometric features and adaptive segments, we are able to adopt efficient indexing methods allowing for flexible and efficient content-based retrieval and browsing in huge motion capture databases. Furthermore, we obtain an efficient preprocessing method substantially accelerating the cost-intensive classical dynamic time warping techniques for the time alignment of logically similar motion data streams. We present experimental results on a test data set of more than one million frames, corresponding to 180 minutes of motion. The linearity of our indexing algorithms guarantees the scalability of our results to much larger data sets.

On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields

Abstract Given a black box which will produce the value of a k -sparse multivariate polynomial for any given specific argument, one may ask for optimal strategies (1) to distinguish such a polynomial from the zero-polynomial, (2) to distinguish any two such polynomials from one other and (3) to (uniformly) reconstruct the polynomial from such an information source. While such strategies are known already for polynomials over fields of characteristic zero, the equally important, but considerably more complicated case of a finite field K of small characteristic is studied in the present paper. The result is that the time complexity of such strategies depends critically on the degree m of the extension field of K from which the arguments are to be chosen; e.g. if m equals the number n of variables, then (1) can be solved by k +1 and (2) as well as (3) by 2 k +1 queries, while in case m = 1 essentially 2 log n ·log k queries are needed.

Fast generalized Fourier transforms

Abstract Let G be a f inite group. Then Ls(G), the linear complexity of a suitable Wedderburn transform corresponding to G, is smaller than 2·|G|2. We improve this trivial upper bound by showing that Ls(G) is smaller than min {(s( T )−l( T ))·|G|+7 q( T ) ·|G| 3 2 , where the minimum is taken over all towers T =(G n >G n−1 >⋯>G 0 ={1}) of subgroups of G=Gn, and where q( T ) (resp. s( T )) is the maximum (resp. sum) of all indices [Gi+1:Gi] corresponding to T and l( T )=n is the length of the tower. A similar upper bound is valid for the linear complexity of the inverse of such a Wedderburn transform. For symmetric groups our technique yields the stronger estimate Ls(Sn)=0(|Sn|·log3|Sn|).

A unified approach to content-based and fault-tolerant music recognition

In this paper, we propose a unified approach to fast index-based music recognition. As an important area within the field of music information retrieval (MIR), the goal of music recognition is, given a database of musical pieces and a query document, to locate all occurrences of that document within the database, up to certain possible errors. In particular, the identification of the query with regard to the database becomes possible. The approach presented in this paper is based on a general algorithmic framework for searching complex patterns of objects in large databases. We describe how this approach may be applied to two important music recognition tasks: The polyphonic (musical score-based) search in polyphonic score data and the identification of pulse-code modulation audio material from a given acoustic waveform. We give an overview on the various aspects of our technology including fault-tolerant search methods. Several areas of application are suggested. We describe several prototypic systems we have developed for those applications including the notify! and the audentify! systems for score- and waveform-based music recognition, respectively.

Shape matching by variational computation of geodesics on a manifold

Klassen et al. [9] recently developed a theoretical formulation to model shape dissimilarities by means of geodesics on appropriate spaces. They used the local geometry of an infinite dimensional manifold to measure the distance dist(A,B) between two given shapes A and B. A key limitation of their approach is that the computation of distances developed in the above work is inherently unstable, the computed distances are in general not symmetric, and the computation times are typically very large. In this paper, we revisit the shooting method of Klassen et al. for their angle-oriented representation. We revisit explicit expressions for the underlying space and we propose a gradient descent algorithm to compute geodesics. In contrast to the shooting method, the proposed variational method is numerically stable, it is by definition symmetric, and it is up to 1000 times faster.

Approximately matching polygonal curves with respect to the Fréchet distance

In this paper we present approximate algorithms for matching two polygonal curves with respect to the Frechet distance. We define a discrete version of the Frechet distance as a distance measure between polygonal curves and show that this discrete version is bounded by the continuous version of the Frechet distance.For the task of matching with respect to the discrete Frechet distance, we develop an algorithm that is based on intersecting certain subsets of the transformation group under consideration. Our algorithm for matching two point sequences of lengths m and n under the group of rigid motions has a time complexity of O(m2n2) for matching under the discrete Frechet distance and can be modified for matching subcurves, closed curves and finding longest common subcurves, Group theoretical considerations allow us to eliminate translation components of affine transformations and to consider matching under arbitrary linear algebraic groups.

Lyrics-based audio retrieval and multimodal navigation in music collections

Modern digital music libraries contain textual, visual, and audio data describing music on various semantic levels. Exploiting the availability of different semantically interrelated representations for a piece of music, this paper presents a query-by-lyrics retrieval system that facilitates multimodal navigation in CD audio collections. In particular, we introduce an automated method to time align given lyrics to an audio recording of the underlying song using a combination of synchronization algorithms. Furthermore, we describe a lyrics search engine and show how the lyrics-audio alignments can be used to directly navigate from the list of query results to the corresponding matching positions within the audio recordings. Finally, we present a user interface for lyrics-based queries and playback of the query results that extends the functionality of our SyncPlayer framework for content-based music and audio navigation.

Multimodal presentation and browsing of music

Recent digitization efforts have led to large music collections, which contain music documents of various modes comprising textual, visual and acoustic data. In this paper, we present a multimodal music player for presenting and browsing digitized music collections consisting of heterogeneous document types. In particular, we concentrate on music documents of two widely used types for representing a musical work, namely visual music representation (scanned images of sheet music) and associated interpretations (audio recordings). We introduce novel user interfaces for multimodal (audio-visual) music presentation as well as intuitive navigation and browsing. Our system offers high quality audio playback with time-synchronous display of the digitized sheet music associated to a musical work. Furthermore, our system enables a user to seamlessly crossfade between various interpretations belonging to the currently selected musical work.

Fast Fourier transforms for symmetric groups: theory and implementation

Recently, it has been proved that a Fourier transform for the symmetric group S, based on Youngs seminormal form can be evaluated in less than 0.5(n3 + n2)n! arithmetic operations. We look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures. We also describe a similarly efficient algorithm for the inverse Fourier transform. We compare the time and memory requirements of our program to those of other existing implementations.

Fast Fourier transforms for metabelian groups

Let G be a finite group . Then