We formulate edge detection as statistical inference. This statistical edge detection is data driven, unlike standard methods for edge detection which are model based. For any set of edge detection filters (implementing local edge cues), we use presegmented images to learn the probability distributions of filter responses conditioned on whether they are evaluated on or off an edge. Edge detection is formulated as a discrimination task specified by a likelihood ratio test on the filter responses. This approach emphasizes the necessity of modeling the image background (the off-edges). We represent the conditional probability distributions nonparametrically and illustrate them on two different data sets of 100 (Sowerby) and 50 (South Florida) images. Multiple edges cues, including chrominance and multiple-scale, are combined by using their joint distributions. Hence, this cue combination is optimal in the statistical sense. We evaluate the effectiveness of different visual cues using the Chernoff information and Receiver Operator Characteristic (ROC) curves. This shows that our approach gives quantitatively better results than the Canny edge detector when the image background contains significant clutter. In addition, it enables us to determine the effectiveness of different edge cues and gives quantitative measures for the advantages of multilevel processing, for the use of chrominance, and for the relative effectiveness of different detectors. Furthermore, we show that we can learn these conditional distributions on one data set and adapt them to the other with only slight degradation of performance without knowing the ground truth on the second data set. This shows that our results are not purely domain specific. We apply the same approach to the spatial grouping of edge cues and obtain analogies to nonmaximal suppression and hysteresis.

We show that generic viewpoint and lighting assumptions resolve standard visual ambiguities by biasing toward planar surfaces. Our model uses orthographic projection with a two-dimensional affine warp and Lambertian reflectance functions, including cast and attached shadows. We use uniform priors on nuisance variables such as viewpoint direction and the light source. Limitations of using uniform priors on nuisance variables are discussed.

We describe a novel viewpoint-lighting ambiguity which we call the KGBR. This ambiguity assumes orthographic projecting or an affine camera, and uses Lambertian reflectance functions including case/attached shadows and multiple light sources. A KGBR transform alters the geometry (by a three-dimensional affine transformation) and albedo properties of objects. If two objects are related by a KGBR transform then for any viewpoint and lighting of the first object there exists a corresponding viewpoint and lighting of the second object so that the images are identical up to an affine transformation. The Generalized Bas Relief (GBR) ambiguity is obtained as a special case of the KGBR. We describe generic viewpoint and lighting assumptions and show that either, or both, resolve this ambiguity by biasing towards objects with planar geometry.

This paper investigates the use of colour and texture cues for segmentation of images within two specified domains. The first is the Sowerby dataset, which contains one hundred colour photographs of country roads in England that have been interactively segmented and classified into six classes-edge, vegetation, air, road, building, and other. The second domain is a set of thirty five-images, taken in San Francisco, which have been interactively segmented into similar classes. In each domain we learn the joint probability distributions of filter responses, based on colour and texture, for each class. These distributions are then used for classification. We restrict ourselves to a limited number of filters in order to ensure that the learnt filter responses do not overfit the training data (our region classes are chosen so as to ensure that there is enough data to avoid over fitting). We do performance analysis on the two datasets by evaluating the false positive and false negative error rates for the classification. This shows that the learnt models achieve high accuracy in classifying individual pixels into those classes for which the filter responses are approximately spatially homogeneous (i.e. road, vegetation, and air but not edge and building). A more sensitive performance measure, the Chernoff information, is calculated in order to quantify how well the cues for edge and building are doing. This demonstrates that statistical knowledge of the domain is a powerful tool for segmentation.

We treat the problem of edge detection as one of statistical inference. Local edge cues, implemented by filters, provide information about the likely positions of edges which can be used as input to higher-level models. Different edge cues can be evaluated by the statistical effectiveness of their corresponding filters evaluated on a dataset of 100 presegmented images. We use information theoretic measures to determine the effectiveness of a variety of different edge detectors working at multiple scales on black and white and color images. Our results give quantitative measures for the advantages of multi-level processing, for the use of chromaticity in addition to greyscale, and for the relative effectiveness of different detectors.