Statistical machine learning is widely used in image classification. However, most techniques (1) require many images to achieve high accuracy and (2) do not provide support for reasoning below the level of classification, and so are unable to support secondary reasoning, such as the existence and position of light sources and other objects outside the image. In recent work an Inductive Logic Programming approach called Logical Vision (LV) was shown to overcome some of these limitations. LV uses Meta-Interpretive Learning combined with low-level extraction of high-contrast points sampled from the image to learn recursive logic programs describing the image. This paper extends LV by using (a) richer background knowledge enabling secondary reasoning from raw images, such as light reflection that can itself be learned and used for resolving visual ambiguities, which cannot be easily modelled using statistical approaches, (b) a wider class of background models representing classical 2D shapes such as circles and ellipses, (c) primitive-level statistical estimators to handle noise in real images. Our results indicate that the new noise-robust version of LV is able to handle secondary reasoning task in real images with few data, which is very similar to scientific discovery process of humans. Specifically, it uses a single example (i.e. one-shot LV) converges to an accuracy at least comparable to thirty-shot statistical machine learner on the prediction of hidden light sources. Moreover, we demonstrate that the learned theory can be used to identify ambiguities in the convexity/concavity of objects such as craters.
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