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

MULTIRIDGELETS FOR TEXTURE ANALYSIS

Directional wavelets have orientation selectivity and thus are able to efficiently represent highly anisotropic elements such as line segments and edges. Ridgelet transform is a kind of directional multi-resolution transform and has been successful in many image processing and texture analysis applications. The objective of this research is to develop multi-ridgelet transform by applying multiwavelet transform to the Radon transform so as to attain attractive improvements. By adapting the cardinal orthogonal multiwavelets to the ridgelet transform, it is shown that the proposed cardinal multiridgelet transform (CMRT) possesses cardinality, approximate translation invariance, and approximate rotation invariance simultaneously, whereas no single ridgelet transform can hold all these properties at the same time. These properties are beneficial to image texture analysis. This is demonstrated in three studies of texture analysis applications. Firstly a texture database retrieval study taking a portion of the Brodatz texture album as an example has demonstrated that the CMRT-based texture representation for database retrieval performed better than other directional wavelet methods. Secondly the study of the LCD mura defect detection was based upon the classification of simulated abnormalities with a linear support vector machine classifier, the CMRT-based analysis of defects were shown to provide efficient features for superior detection performance than other competitive methods. Lastly and the most importantly, a study on the prostate cancer tissue image classification was conducted. With the CMRT-based texture extraction, Gaussian kernel support vector machines have been developed to discriminate prostate cancer Gleason grade 3 versus grade 4. Based on a limited database of prostate specimens, one classifier was trained to have remarkable test performance. This approach is unquestionably promising and is worthy to be fully developed

Texture representation using wavelet filterbanks

Texture analysis is a fundamental issue in image analysis and computer vision. While considerable research has been carried out in the texture analysis domain, problems relating to texture representation have been addressed only partially and active research is continuing. The vast majority of algorithms for texture analysis make either an explicit or implicit assumption that all images are captured under the same measurement conditions, such as orientation and illumination. These assumptions are often unrealistic in many practical applications;This dissertation addresses the viewpoint-invariance problem in texture classification by introducing a rotated wavelet filterbank. The proposed filterbank, in conjunction with a standard wavelet filterbank, provides better freedom of orientation tuning for texture analysis. This allows one to obtain texture features that are invariant with respect to texture rotation and linear grayscale transformation. In this study, energy estimates of channel outputs that are commonly used as texture features in texture classification are transformed into a set of viewpoint-invariant features. Texture properties that have a physical connection with human perception are taken into account in the transformation of the energy estimates;Experiments using natural texture image sets that have been used for evaluating other successful approaches were conducted in order to facilitate comparison. We observe that the proposed feature set outperformed methods proposed by others in the past. A channel selection method is also proposed to minimize the computational complexity and improve performance in a texture segmentation algorithm. Results demonstrating the validity of the approach are presented using experimental ultrasound tendon images

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Packets Wavelets and Stockwell Transform Analysis of Femoral Doppler Ultrasound Signals

Ultrasonic Doppler signals are widely used in the detection of cardiovascular pathologies or the evaluation of the degree of stenosis in the femoral arteries. The presence of stenosis can be indicated by disturbing the blood flow in the femoral arteries, causing spectral broadening of the Doppler signal. To analyze these types of signals and determine stenosis index, a number of time-frequency methods have been developed, such as the short-time Fourier transform, the continuous wavelets transform, the wavelet packet transform, and the S-transform

Meningioma classification using an adaptive discriminant wavelet packet transform

Meningioma subtypes classification is a real world problem from the domain of histological image analysis that requires new methods for its resolution. Computerised histopathology presents a whole new set of problems and introduces new challenges in image classification. High intra-class variation and low inter-class differences in textures is often an issue in histological image analysis problems such as Meningioma subtypes classification. In this thesis, we present an adaptive wavelets based technique that adapts to the variation in the texture of meningioma samples and provides high classification accuracy results. The technique provides a mechanism for attaining an image representation consisting of various spatial frequency resolutions that represent the image and are referred to as subbands. Each subband provides different information pertaining to the texture in the image sample. Our novel method, the Adaptive Discriminant Wavelet Packet Transform (ADWPT), provides a means for selecting the most useful subbands and hence, achieves feature selection. It also provides a mechanism for ranking features based upon the discrimination power of a subband. The more discriminant a subband, the better it is for classification. The results show that high classification accuracies are obtained by selecting subbands with high discrimination power. Moreover, subbands that are more stable i.e. have a higher probability of being selected provide better classification accuracies. Stability and discrimination power have been shown to have a direct relationship with classification accuracy. Hence, ADWPT acquires a subset of subbands that provide a highly discriminant and robust set of features for Meningioma subtype classification. Classification accuracies obtained are greater than 90% for most Meningioma subtypes. Consequently, ADWPT is a robust and adaptive technique which enables it to overcome the issue of high intra-class variation by statistically selecting the most useful subbands for meningioma subtype classification. It overcomes the issue of low inter-class variation by adapting to texture samples and extracting the subbands that are best for differentiating between the various meningioma subtype textures

Learning the Morphological Diversity

International audienceThis article proposes a new method for image separation into a linear combination of morphological components. Sparsity in global dictionaries is used to extract the cartoon and oscillating content of the image. Complicated texture patterns are extracted by learning adapted local dictionaries that sparsify patches in the image. These global and local sparsity priors together with the data fidelity define a non-convex energy and the separation is obtained as a stationary point of this energy. This variational optimization is extended to solve more general inverse problems such as inpainting. A new adaptive morphological component analysis algorithm is derived to find a stationary point of the energy. Using adapted dictionaries learned from data allows to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial to capture complex texture patterns