Continuous dimensionality characterization of image structures

Abstract

Intrinsic dimensionality is a concept introduced by statistics and later used in image processing to measure the dimensionality of a data set. In this paper, we introduce a continuous representation of the intrinsic dimension of an image patch in terms of its local spectrum or, equivalently, its gradient field. By making use of a cone structure and barycentric co-ordinates, we can associate three confidences to the three different ideal cases of intrinsic dimensions corresponding to homogeneous image patches, edge-like structures and junctions. The main novelty of our approach is the representation of confidences as prior probabilities which can be used within a probabilistic framework. To show the potential of our continuous representation, we highlight applications in various contexts such as image structure classification, feature detection and localisation, visual scene statistics and optic flow evaluation.

Using surfaces and surface relations in an Early Cognitive Vision system

“…The confidence B e indicates the likelihood that the local image structure corresponds to an edge (for details, see [15]). …”

“…Therefore, a 2D texlet is extracted from a position in the image, if a specified area around the sampling point is classified as containing texture [15]. This simple 2D feature only consist of a point in image coordinates and some basic appearance information.…”

Autocorrelation-Driven Diffusion Filtering

“…where σ 2 e is the estimated noise variance according to the method described in [23] with a minor modification. The estimation is based on a mixture of two χ 2 2 distributions, which are fitted to the squared gradient magnitude distribution using the EM algorithm.…”

“…Flat structures should be diffused isotropically, linear structures only in one direction, and two-dimensional structures not at all. Furthermore, we derive new discrete filter masks, apply a new noise estimation method [23], and extend the experimental evaluation using methods that take into account the visual quality: the visual information fidelity (VIF) [24] and the structural similarity index (SSIM) [25].…”

Adaptive Filtering Using Channel Representations

“…A further aspect of adaptive filtering is the choice of the smoothing kernels, depending on the noise level [10] (for related work on noise level estimation, see also [17,48]) and the noise distribution, e.g., multiplicative noise [49]. The selection of filter kernels is however out of the scope of this review and the interested reader is referred to the original publications.…”