Jussi T. Lindgren

Spatial dependencies between local luminance and contrast in natural images.

Previous research has suggested only weak statistical dependencies between local luminance and contrast in natural images. Here we study luminance and contrast in natural images using established measures and show that when multiple measurements of these two local quantities are taken in different spatial locations across the visual field, strong dependencies are revealed that were not apparent in previous pointwise (single-site) analyses. We present a few simple experiments demonstrating this spatial dependency of luminance and contrast and show that the luminance measurements can be used to approximate the contrast measurements. We also show that relying on higher-order statistics, independent component analysis learns paired spatial features for luminance and contrast. These features are shown to share orientation and localization, with the filters corresponding to the features dependent in their outputs. Finally, we demonstrate that the found dependencies also exist in artificial images generated from a dead leaves model, implying that simple image phenomena may suffice to account for the dependencies. Our results indicate that local luminance and contrast computations do not recover independent information sources from the visual signal. Subsequently, our results predict spatial processing of local luminance and contrast to be non-separable in visual systems.

Estimating Markov Random Field Potentials for Natural Images

A magnetic recording medium which comprises a non-magnetic support, a magnetic recording layer formed on one side of the support, and a back coat layer formed on the other side. The back coat layer is made of a dispersion, in a binder resin, of non-magnetic particles on which there is adsorbed carbon black having an average size not larger than 100 millimicrons and a specific surface area not less than 30 m2/g.

Learning high-level independent components of images through a spectral representation

Statistical methods, such as independent component analysis, have been successful in learning local low-level features from natural image data. Here we extend these methods for learning high-level representations of whole images or scenes. We show empirically that independent component analysis is able to capture some intuitive natural image categories when applied on histograms of outputs of ordinary Gabor-like filters. This can be taken as an indication that maximizing the independence or sparseness of features may be a meaningful strategy even on higher levels of image processing, for such advanced functionality as object recognition or image retrieval from databases.

The statistical properties of local log-contrast in natural images

The study of natural image statistics considers the statistical properties of large collections of images from natural scenes, and has applications in image processing, computer vision, and visual computational neuroscience. In the past, a major focus in the field of natural image statistics have been the statistics of outputs of linear filters. Recently, attention has been turning to nonlinear models. The contribution of this paper is the empirical analysis of the statistical properties of a central nonlinear property of natural scenes: the local log-contrast. To this end, we have studied both second-order and higher-order statistics of local log-contrast. Second-order statistics can be observed from the average amplitude spectrum. To examine higher-order statistics, we applied a higher-order-statistics-based model called independent component analysis to images of local log-contrast. Our results on second-order statistics show that the local log-contrast has a power-law-like average amplitude spectrum, similarly as the original luminance data. As for the higher-order statistics, we show that they can be utilized to learn intuitively meaningful spatial local-contrast patterns, such as contrast edges and bars. In addition to shedding light on the fundamental statistical properties of natural images, our results have important consequences for the analysis and design of multilayer statistical models of natural image data. In particular, our results show that in the case of local log-contrast, oriented and localized second-layer linear operators can be learned from the higher-order statistics of the nonlinearly mapped output of the first layer.

Online Learning of Discriminative Patterns from Unlimited Sequences of Candidates

Recent research in object recognition has demonstrated the advantages of representing objects and scenes through localized patterns such as small image templates. In this paper we study the selection of patterns in the framework of extended supervised online learning, where not only new examples but also new candidate patterns become available over time. We propose an algorithm that maintains a pool of discriminative patterns and improves the quality of the pool in a disciplined manner over time. The proposed algorithm is not tied to any specific pattern type or data domain. We evaluate the method on several object detection tasks

On the learning of nonlinear visual features from natural images by optimizing response energies

The operation of V1 simple cells in primates has been traditionally modelled with linear models resembling Gabor filters, whereas the functionality of subsequent visual cortical areas is less well understood. Here we explore the learning of mechanisms for further nonlinear processing by assuming a functional form of a product of two linear filter responses, and estimating a basis for the given visual data by optimizing for robust alternative of variance of the nonlinear model outputs. By a simple transformation of the learned model, we demonstrate that on natural images, both minimization and maximization in our setting lead to oriented, band-pass and localized linear filters whose responses are then nonlinearly combined. In minimization, the method learns to multiply the responses of two Gabor-like filters, whereas in maximization it learns to subtract the response magnitudes of two Gabor-like filters. Empirically, these learned nonlinear filters appear to function as conjunction detectors and as opponent orientation filters, respectively. We provide a preliminary explanation for our results in terms of filter energy correlations and fourth power optimization.

Unsupervised learning of dependencies between local luminance and contrast in natural images

Separate processing of local luminance and contrast in biological visual systems has been argued to be due to the independence of these two properties in natural image data. In this paper we examine spatial, retinotopic channels formed by these two quantities and use Independent Component Analysis to study the possible dependencies between the channels. As a result, oriented, localized bandpass filter pairs are learned, where one filter processes the luminance channel and the other the contrast channel. We study the relationship of the learned filters and their pairings, and show that these are due to dependencies existing between local luminance and contrast. Subsequently, our results suggest that the separate processing of local luminance and contrast can not be attributed to their independence in natural images.

Experiments with Projection Learning

Excessive information is known to degrade the classification performance of many machine learning algorithms. Attribute-efficient learning algorithms can tolerate irrelevant attributes without their performance being affected too much. Valiants projection learning is a way to combine such algorithms so that this desired property is maintained. The archetype attribute-efficient learning algorithm Winnow and, especially, combinations of Winnow have turned out empirically successful in domains containing many attributes. However, projection learning as proposed by Valiant has not yet been evaluated empirically. We study how projection learning relates to using Winnow as such and with an extended set of attributes. We also compare projection learning with decision tree learning and Naive Bayes on UCI data sets.Projection learning systematically enhances the classification accuracy of Winnow, but the cost in time and space consumption can be high. Balanced Winnow seems to be a better alternative than the basic algorithm for learning the projection hypotheses. However, Balanced Winnow is not well suited for learning the second level (projective disjunction) hypothesis. The on-line approach projection learning does not fall far behind in classification accuracy from batch algorithms such as decision tree learning and Naive Bayes on the UCI data sets that we used.