Analogical reasoning is a powerful inductive mechanism, widely used in human cognition and increasingly applied in artificial intelligence. Formal frameworks for analogical inference have been developed for Boolean domains, where inference is provably sound for affine functions and approximately correct for functions close to affine. These results have informed the design of analogy-based classifiers. However, they do not extend to regression tasks or continuous domains. In this paper, we revisit analogical inference from a foundational perspective. We first present a counterexample showing that existing generalization bounds fail even in the Boolean setting. We then introduce a unified framework for analogical reasoning in real-valued domains based on parameterized analogies defined via generalized means. This model subsumes both Boolean classification and regression, and supports analogical inference over continuous functions. We characterize the class of analogy-preserving functions in this setting and derive both worst-case and average-case error bounds under smoothness assumptions. Our results offer a general theory of analogical inference across discrete and continuous domains.

This paper describes a robust depth estimation algorithm for multi-focus plenoptic images. The main feature of the proposed method consists of a hybrid template matching scheme built-upon intensity and local phase information, which adapts to the blurriness of neighbouring lenslet microimages. By reducing the impact of defocusblur on the template matching accuracy, the proposed method efficiently handles the varying triangulation baseline over the depth-of-field, thus discarding the need for scene-related information such as the expected range of disparities. Experimental results demonstrate the robustness of the proposed method over the most used commercially available depth estimation algorithm, achieving a reduction of 73% on the depth estimation error.