The vanishing ideal of a set of n points S, is the set of all polynomials that attain the value of zero on all the points in S. Such ideals can be compactly represented using a small set of polynomials known as generators of the ideal. Here we describe and analyze an efficient procedure that constructs a set of generators of a vanishing ideal. Our procedure is numerically stable, and can be used to find approximately vanishing polynomials. The resulting polynomials capture nonlinear structure in data, and can for example be used within supervised learning. Empirical comparison with kernel methods show that our method constructs more compact classifiers with comparable accuracy.

Human observers understand the content of an image intuitively. Based upon image content, they perform many image-related tasks, such as creating slide shows and photo albums, and organizing their image archives. For example, to select photos for an album, people assess image quality based upon the main objects in the image. They modify colors in an image based upon the color of important objects, such as sky, grass or skin. Serious photographers might modify each object separately. Photo applications, in contrast, use low-level descriptors to guide similar tasks. Typical descriptors, such as color histograms, noise level, JPEG artifacts and overall sharpness, can guide an imaging application and safeguard against blunders. However, there is a gap between the outcome of such operations and the same task performed by a person. We believe that the gap can be bridged by automatically understanding the content of the image. This paper presents algorithms for automatic tagging of perceptual objects in images, including sky, skin, and foliage, which constitutes an important step toward this goal.

Print quality (PQ) is a composite attribute defined by human perception. As such, the ultimate way to determine and quantify PQ is by human survey. However, repeated surveys are time consuming and often represent a burden on processes that involve repeated evaluations. A desired alternative would be an automatic quality rating tool. Once such quality evaluation measure is proposed, it should be qualified. That is, it should be shown to reflect human assessment. If two of the human opinions conflict, the tool cannot possibly agree with both. Conflicts between human opinions are common, which complicates the evaluation of tool's success in reflecting human judgment. There are many optional ways for measuring the agreement between human assessment and tool evaluation, but different methods may have conflicting results. It is, therefore, important to pre-establish the appropriate method for the evaluation of quality-evaluation-tools, a method that takes the disagreement among the survey participants into account. In this paper, we model human quality preference and derive the most appropriate method to qualify quality evaluation tools. We demonstrate the resulting qualification method in a real life scenario-the qualification of the mechanical band meter.