We introduce a simple modification of local image descriptors, such as SIFT, based on pooling gradient orientations across different domain sizes, in addition to spatial locations. The resulting descriptor, which we call DSP-SIFT, outperforms other methods in wide-baseline matching benchmarks, including those based on convolutional neural networks, despite having the same dimension of SIFT and requiring no training.
 Many modern visual recognition algorithms incorporate a step of spatial 'pooling', where the outputs of several nearby feature detectors are combined into a local or global 'bag of features', in a way that preserves task-related information while removing irrelevant details. Pooling is used to achieve invariance to image transformations, more compact representations, and better robustness to noise and clutter. Several papers have shown that the details of the pooling operation can greatly influence the performance, but studies have so far been purely empirical. In this paper, we show that the reasons underlying the performance of various pooling methods are obscured by several confounding factors, such as the link between the sample cardinality in a spatial pool and the resolution at which low-level features have been extracted. We provide a detailed theoretical analysis of max pooling and average pooling, and give extensive empirical comparisons for object recognition tasks. We frame the problem of local representation of imaging data as the computation of minimal sufficient statistics that are invariant to nuisance variability induced by viewpoint and illumination. We show that, under very stringent conditions, these are related to “feature descriptors” commonly used in Computer Vision. Such conditions can be relaxed if multiple views of the same scene are available. We propose a sampling-based and a point-estimate based approximation of such a representation, compared empirically on image-to-(multiple)image matching, for which we introduce a multi-view wide-baseline matching benchmark, consisting of a mixture of real and synthetic objects with ground truth camera motion and dense three-dimensional geometry.