Natural Image Coding in V1: How Much Use is Orientation Selectivity?

Orientation selectivity is the most striking feature of simple cell coding in V1 which has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. In order to assess the tenability of this hypothesis, it is an important empirical question how much more redundancies can be removed with ICA in comparison to PCA, or other second-order decorrelation methods. This question has not yet been settled, as over the last ten years contradicting results have been reported ranging from less than five to more than hundred percent extra gain for ICA. Here, we aim at resolving this conflict by presenting a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss we compute, for the first time, complete rate-distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is surprisingly small. Furthermore, we show that a simple spherically symmetric distribution with only two parameters can fit the data even better than the probabilistic model underlying ICA. Since spherically symmetric models are agnostic with respect to the specific filter shapes, we conlude that orientation selectivity is unlikely to play a critical role for redundancy reduction

Unsupervised and supervised approaches to color space transformation for image coding

The linear transformation of input (typically RGB) data into a color space is important in image compression. Most schemes adopt fixed transforms to decorrelate the color channels. Energy compaction transforms such as the Karhunen-Loève (KLT) do entail a complexity increase. Here, we propose a new data-dependent transform (aKLT), that achieves compression performance comparable to the KLT, at a fraction of the computational complexity. More important, we also consider an application-aware setting, in which a classifier analyzes reconstructed images at the receiver's end. In this context, KLT-based approaches may not be optimal and transforms that maximize post-compression classifier performance are more suited. Relaxing energy compactness constraints, we propose for the first time a transform which can be found offline optimizing the Fisher discrimination criterion in a supervised fashion. In lieu of channel decorrelation, we obtain spatial decorrelation using the same color transform as a rudimentary classifier to detect objects of interest in the input image without adding any computational cost. We achieve higher savings encoding these regions at a higher quality, when combined with region-of-interest capable encoders, such as JPEG 2000

Processing of natural temporal stimuli by macaque retinal ganglion cells

This study quantifies the performance of primate retinal ganglion cells in response to natural stimuli. Stimuli were confined to the temporal and chromatic domains and were derived from two contrasting environments, one typically northern European and the other a flower show. The performance of the cells was evaluated by investigating variability of cell responses to repeated stimulus presentations and by comparing measured to model responses. Both analyses yielded a quantity called the coherence rate (in bits per second), which is related to the information rate. Magnocellular (MC) cells yielded coherence rates of up to 100 bits/sec, rates of parvocellular (PC) cells were much lower, and short wavelength (S)-cone-driven ganglion cells yielded intermediate rates. The modeling approach showed that for MC cells, coherence rates were generated almost exclusively by the luminance content of the stimulus. Coherence rates of PC cells were also dominated by achromatic content. This is a consequence of the stimulus structure; luminance varied much more in the natural environment than chromaticity. Only approximately one-sixth of the coherence rate of the PC cells derived from chromatic content, and it was dominated by frequencies below 10 Hz. S-cone-driven ganglion cells also yielded coherence rates dominated by low frequencies. Below 2–3 Hz, PC cell signals contained more power than those of MC cells. Response variation between individual ganglion cells of a particular class was analyzed by constructing generic cells, the properties of which may be relevant for performance higher in the visual system. The approach used here helps define retinal modules useful for studies of higher visual processing of natural stimuli

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics