On Affine Invariant Descriptors Related to SIFT

Abstract

Using a classical result on algebraic invariants of the unimodular group, we present in this paper some basic geometric affine invariant quantities, and we use them to construct some distinctive descriptors for object detection. Although full affine invariance cannot be guaranteed due to noncommutativity of camera blur with affine maps and the domain problem (that is, the difficulty of finding an affine covariant domain), the proposed descriptors behave more robustly than SIFT with respect to affine deformations. This is supported by our comparisons both with the version of SIFT computed on an affine normalized neighborhood, and with ASIFT, which solves both the previously mentioned camera blur and domain problems by cleverly sampling the orbit of affine transformations of the images.

An Analysis of the Factors Affecting Keypoint Stability in Scale-Space

“…Finally, the gradient orientation distribution in this patch is encoded into a 128 elements feature, the so-called SIFT descriptor. We shall not discuss further the constitution of the descriptor and refer to the abundant literature [35,30,36,17,33,18]. For a detailed description of the SIFT method we refer the reader to [37].…”

“…The literature on SIFT focuses on variants, alternatives and accelerations [3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. A majority of them use the scale-space keypoints as defined in the SIFT method.…”

An analysis of scale-space sampling in SIFT

“…Finally, the gradient orientation distribution in this patch is coded into a 128 elements feature, the so-called SIFT descriptor. We shall not discuss further the constitution of the descriptor and refer to the abundant literature [17,18,30,[33][34][35].…”

Two-view matching with view synthesis revisited

“…Pang et al [21] replaced SIFT by SURF [3] in the ASIFT algorithm to reduce the computation time. Sadek et al [23] present a new affine covariant descriptor based on SIFT which can be used with or without view synthesis. Detection of the MSERs on the scale space pyramid was proposed by Forssén and Lowe [9].…”