For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a local Mahalanobis metric per datum, and show how we can learn a local invariant metric to any transformation in order to improve performance.
The most common way to achieve invariance, or at least insensitivity, to a transformation in computer vision applications is by using hand-crafted descriptors such as SIFT @cite_7 or HOG @cite_0 . Another way, used in convolutional networks @cite_14 , is by adding pooling and subsampling forcing the net to be insensitive to small translations. It is important to note that transformations such as rotations have a global behaviour, i.e. there is a global consistency between the pixel movement. This global consistency is not totally captured by the pooling and subsampling. As we will see in our experiments, using an invariant metric can be useful even when working with robust features such as HOG.
@cite_0 @cite_14 @cite_7
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Descriptors based on orientation histograms are widely used in computer vision. The spatial pooling involved in these representations provides important invariance properties, yet it is also responsible for the loss of important details. In this paper, we suggest a way to preserve the details described by the local curvature. We propose a descriptor that comprises the direction and magnitude of curvature and naturally expands classical orientation histograms like SIFT and HOG. We demonstrate the general benefit of the expansion exemplarily for image classification, object detection, and descriptor matching. Convolutional Neural Network (CNN) features have been successfully employed in recent works as an image descriptor for various vision tasks. But the inability of the deep CNN features to exhibit invariance to geometric transformations and object compositions poses a great challenge for image search. In this work, we demonstrate the effectiveness of the objectness prior over the deep CNN features of image regions for obtaining an invariant image representation. The proposed approach represents the image as a vector of pooled CNN features describing the underlying objects. This representation provides robustness to spatial layout of the objects in the scene and achieves invariance to general geometric transformations, such as translation, rotation and scaling. The proposed approach also leads to a compact representation of the scene, making each image occupy a smaller memory footprint. Experiments show that the proposed representation achieves state of the art retrieval results on a set of challenging benchmark image datasets, while maintaining a compact representation. Representations that are invariant to translation, scale and other transformations, can considerably reduce the sample complexity of learning, allowing recognition of new object classes from very few examples|a hallmark of human recognition. Empirical estimates of one-dimensional projections of the distribution induced by a group of ane transformations are proven to represent a unique and invariant signature associated with an image. We show how projections yielding invariant signatures for future images can be learned automatically, and updated continuously, during unsupervised visual experience. A module performing ltering and pooling, like simple and complex cells as proposed by Hubel and Wiesel, can compute such estimates. Under this view, a pooling stage estimates a one-dimensional probability distribution. Invariance from observations through a restricted window is equivalent to a sparsity property w.r.t. to a transformation, which yields templates that are a) Gabor for optimal simultaneous invariance to translation and scale or b) very specic for complex, class-dependent transformations such as rotation in depth of faces. Hierarchical architectures consisting of this basic Hubel-Wiesel module inherit its properties of invariance, stability, and discriminability while capturing the compositional organization of the visual world in terms of wholes and parts, and are invariant to complex transformations that may only be locally ane. The theory applies to several existing deep learning convolutional architectures for image and speech recognition. It also suggests that the main computational goal of the ventral stream of visual cortex is to provide a hierarchical representation of ne