A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Orthonormal Shift-Invariant Adaptive Local Trigonometric Decomposition

In this paper, an extended library of smooth local trigonometric bases is defined, and an appropriate fast "best-basis" search algorithm is introduced. When compared with the standard local cosine decomposition (LCD), the proposed algorithm is advantageous in three respects. First, it leads to a best-basis expansion that is shift-invariant. Second, the resulting representation is characterized by a lower information cost. Third, the polarity of the folding operator is adapted to the parity properties of the segmented signal at the end-points. The shift-invariance stems from an adaptive relative shift of expansions in distinct resolution levels. We show that at any resolution level ` it suffices to examine and select one of two relative shift options --- a zero shift or a 2 \Gamma`\Gamma1 shift. A variable folding operator, whose polarity is locally adapted to the parity properties of the signal, further enhances the representation. The computational complexity is manageable and compa..

Wavelet-based techniques for speech recognition

In this thesis, new wavelet-based techniques have been developed for the extraction of features from speech signals for the purpose of automatic speech recognition (ASR). One of the advantages of the wavelet transform over the short time Fourier transform (STFT) is its capability to process non-stationary signals. Since speech signals are not strictly stationary the wavelet transform is a better choice for time-frequency transformation of these signals. In addition it has compactly supported basis functions, thereby reducing the amount of computation as opposed to STFT where an overlapping window is needed. [Continues.

Wavelet methods in speech recognition

In this thesis, novel wavelet techniques are developed to improve parametrization of speech signals prior to classification. It is shown that non-linear operations carried out in the wavelet domain improve the performance of a speech classifier and consistently outperform classical Fourier methods. This is because of the localised nature of the wavelet, which captures correspondingly well-localised time-frequency features within the speech signal. Furthermore, by taking advantage of the approximation ability of wavelets, efficient representation of the non-stationarity inherent in speech can be achieved in a relatively small number of expansion coefficients. This is an attractive option when faced with the so-called 'Curse of Dimensionality' problem of multivariate classifiers such as Linear Discriminant Analysis (LDA) or Artificial Neural Networks (ANNs). Conventional time-frequency analysis methods such as the Discrete Fourier Transform either miss irregular signal structures and transients due to spectral smearing or require a large number of coefficients to represent such characteristics efficiently. Wavelet theory offers an alternative insight in the representation of these types of signals. As an extension to the standard wavelet transform, adaptive libraries of wavelet and cosine packets are introduced which increase the flexibility of the transform. This approach is observed to be yet more suitable for the highly variable nature of speech signals in that it results in a time-frequency sampled grid that is well adapted to irregularities and transients. They result in a corresponding reduction in the misclassification rate of the recognition system. However, this is necessarily at the expense of added computing time. Finally, a framework based on adaptive time-frequency libraries is developed which invokes the final classifier to choose the nature of the resolution for a given classification problem. The classifier then performs dimensionaIity reduction on the transformed signal by choosing the top few features based on their discriminant power. This approach is compared and contrasted to an existing discriminant wavelet feature extractor. The overall conclusions of the thesis are that wavelets and their relatives are capable of extracting useful features for speech classification problems. The use of adaptive wavelet transforms provides the flexibility within which powerful feature extractors can be designed for these types of application