R.M. Figueras i Ventura

Low-rate and flexible image coding with redundant representations

New breakthroughs in image coding possibly lie in signal decomposition through nonseparable basis functions that can efficiently capture edge characteristics, present in natural images. The work proposed in this paper provides an adaptive way of representing images as a sum of two-dimensional features. It presents a low bit-rate image coding method based on a matching pursuit (MP) expansion, over a dictionary built on anisotropic refinement and rotation of contour-like atoms. This method is shown to provide, at low bit rates, results comparable to the state of the art in image compression, represented here by JPEG2000 and SPIHT, with generally a better visual quality in the MP scheme. The coding artifacts are less annoying than the ringing introduced by wavelets at very low bit rate, due to the smoothing performed by the basis functions used in the MP algorithm. In addition to good compression performances at low bit rates, the new coder has the advantage of producing highly flexible streams. They can easily be decoded at any spatial resolution, different from the original image, and the bitstream can be truncated at any point to match diverse bandwidth requirements. The spatial adaptivity is shown to be more flexible and less complex than transcoding operations generally applied to state of the art codec bitstreams. Due to both its ability for capturing the most important parts of multidimensional signals, and a flexible stream structure, the image coder proposed in this paper represents an interesting solution for low to medium rate image coding in visual communication applications.

A posteriori quantization of progressive matching pursuit streams

This paper proposes a rate-distortion optimal a posteriori quantization scheme for matching pursuit (MP) coefficients. The a posteriori quantization applies to an MP expansion that has been generated offline and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise. The redundancy of the MP dictionary provides an indicator of the relative importance of coefficients and atom indices and, subsequently, on the quantization error. It is used to define a universal upper bound on the decay of the coefficients, sorted in decreasing order of magnitude. A new quantization scheme is then derived, where this bound is used as an Oracle for the design of an optimal a posteriori quantizer. The latter turns the exponentially distributed coefficient entropy-constrained quantization problem into a simple uniform quantization problem. Using simulations with random dictionaries, we show that the proposed exponentially upper bounded quantization (EUQ) clearly outperforms classical schemes. Stepping on the ideal Oracle-based approach, a suboptimal adaptive scheme is then designed that approximates the EUQ but still outperforms competing quantization methods in terms of rate-distortion characteristics. Finally, the proposed quantization method is studied in the context of image coding. It performs similarly to state-of-the-art coding methods (and even better at low rates) while interestingly providing a progressive stream that is very easy to transcode and adapt to changing rate constraints.

Color image scalable coding with matching pursuit

The paper presents a new scalable and highly flexible color image coder based on a matching pursuit expansion. The matching pursuit algorithm provides an intrinsically progressive stream and the proposed coder allows us to reconstruct color information from the first bit received. In order to capture edges in natural images efficiently, the dictionary of atoms is built by translation, rotation and anisotropic refinement of a wavelet-like mother function. This dictionary is moreover invariant under shifts and isotropic scaling, thus leading to very simple spatial resizing operations. This flexibility and adaptivity of the MP coder makes it appropriate for asymmetric applications with heterogeneous end user terminals.

MPEG-7 camera

An MPEG-7 camera extends the capabilities of conventional cameras by analyzing its scene in order to generate a content-based description according to the recently approved MPEG-7 standard. This gives to the camera a large variety of current and potential applications, such as surveillance, augmented reality, and virtual display. This paper provides an overview of what is meant by an MPEG-7 camera, discusses the above mentioned applications, and provides an implementation example of such a camera using existing hardware products.

R-D analysis of adaptive edge representations

This paper presents a rate-distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed on this kind of image, giving a toy model for a non-linear adaptive coding technique, and its rate-distortion behavior is studied. The effect of refining the quadtree decomposition is also analyzed.

Statistically Driven Sparse Image Approximation

Finding the sparsest approximation of an image as a sum of basis functions drawn from a redundant dictionary is an NP-hard problem. In the case of a dictionary whose elements form an overcomplete basis, a recently developed method, based on alternating thresholding and projection operations, provides an appealing approximate solution. When applied to images, this method produces sparser results and requires less computation than current alternative methods. Motivated by recent developments in statistical image modeling, we develop an enhancement of this method based on a locally adaptive threshold operation, and demonstrate that the enhanced algorithm is capable of finding sparser approximations with a decrease in computational complexity.

Contextually adaptive signal representation using conditional principal component analysis

The conventional method of generating a basis that is optimally adapted (in MSE) for representation of an ensemble of signals is principal component analysis (PCA). A more ambitious modern goal is the construction of bases that are adapted to individual signal instances. Here we develop a new framework for instance-adaptive signal representation by exploiting the fact that many real-world signals exhibit local self-similarity. Specifically, we decompose the signal into multiscale subbands, and then represent local blocks of each subband using basis functions that are linearly derived from the surrounding context. The linear mappings that generate these basis functions are learned sequentially, with each one optimized to account for as much variance as possible in the local blocks. We apply this methodology to learning a coarse-to-fine representation of images within a multi-scale basis, demonstrating that the adaptive basis can account for significantly more variance than a PCA basis of the same dimensionality.