Scale-space for discrete signals

A basic and extensive treatment of discrete aspects of the scale-space theory is presented. A genuinely discrete scale-space theory is developed and its connection to the continuous scale-space theory is explained. Special attention is given to discretization effects, which occur when results from the continuous scale-space theory are to be implemented computationally. The 1D problem is solved completely in an axiomatic manner. For the 2D problem, the author discusses how the 2D discrete scale space should be constructed. The main results are as follows: the proper way to apply the scale-space theory to discrete signals and discrete images is by discretization of the diffusion equation, not the convolution integral; the discrete scale space obtained in this way can be described by convolution with the kernel, which is the discrete analog of the Gaussian kernel, a scale-space implementation based on the sampled Gaussian kernel might lead to undesirable effects and computational problems, especially at fine levels of scale; the 1D discrete smoothing transformations can be characterized exactly and a complete catalogue is given; all finite support 1D discrete smoothing transformations arise from repeated averaging over two adjacent elements (the limit case of such an averaging process is described); and the symmetric 1D discrete smoothing kernels are nonnegative and unimodal, in both the spatial and the frequency domain     

Scale-Invariant Scale-Channel Networks: Deep Networks That Generalise to Previously Unseen Scales

Journal of Mathematical Imaging and Vision - The ability to handle large scale variations is crucial for many real-world visual tasks. A straightforward approach for handling scale in a deep...     

Scale Selection Properties of Generalized Scale-Space Interest Point Detectors

Scale-invariant interest points have found several highly successful applications in computer vision, in particular for image-based matching and recognition. This paper presents a theoretical analysis of the scale selection properties of a generalized framework for detecting interest points from scale-space features presented in Lindeberg (Int. J. Comput. Vis. 2010, under revision) and comprising:

an enriched set of differential interest operators at a fixed scale including the Laplacian operator, the determinant of the Hessian, the new Hessian feature strength measures I and II and the rescaled level curve curvature operator, as well as

an enriched set of scale selection mechanisms including scale selection based on local extrema over scale, complementary post-smoothing after the computation of non-linear differential invariants and scale selection based on weighted averaging of scale values along feature trajectories over scale.

It is shown how the selected scales of different linear and non-linear interest point detectors can be analyzed for Gaussian blob models. Specifically it is shown that for a rotationally symmetric Gaussian blob model, the scale estimates obtained by weighted scale selection will be similar to the scale estimates obtained from local extrema over scale of scale normalized derivatives for each one of the pure second-order operators. In this respect, no scale compensation is needed between the two types of scale selection approaches. When using post-smoothing, the scale estimates may, however, be different between different types of interest point operators, and it is shown how relative calibration factors can be derived to enable comparable scale estimates for each purely second-order operator and for different amounts of self-similar post-smoothing. A theoretical analysis of the sensitivity to affine image deformations is presented, and it is shown that the scale estimates obtained from the determinant of the Hessian operator are affine covariant for an anisotropic Gaussian blob model. Among the other purely second-order operators, the Hessian feature strength measure I has the lowest sensitivity to non-uniform scaling transformations, followed by the Laplacian operator and the Hessian feature strength measure II. The predictions from this theoretical analysis agree with experimental results of the repeatability properties of the different interest point detectors under affine and perspective transformations of real image data. A number of less complete results are derived for the level curve curvature operator.     

Age relations of cardiovascular risk factors in a traditional Melanesian society: the Kitava Study

This study examined cross-sectional age relations of blood pressure, anthropometric indexes, serum lipids, and hemostatic variables in 203 subsistence horticulturists aged 20-86 y in Kitava, Trobriand Islands, Papua New Guinea. The population is characterized by extreme leanness (despite food abundance), low blood pressure, low plasma plasminogen activator inhibitor 1 activity, and rarity of cardiovascular disease. Tubers, fruit, fish, and coconut are dietary staples whereas dairy products, refined fat and sugar, cereals, and alcohol are absent and salt intake is low. Although diastolic blood pressure was not associated with age in Kitavans, systolic blood pressure increased linearly after 50 y of age in both sexes. Body mass index decreased with age in both sexes. Serum total cholesterol, triacylglycerol, low-density-lipoprotein cholesterol, and apolipoprotein B increased in males between 20 and 50 y of age, whereas high-density-lipoprotein cholesterol and apolipoprotein A-I decreased. There were no significant differences in these indexes with age in the few females studied. A slight linear age-related increase of lipoprotein(a) was present in males. Plasma fibrinogen, factor VII clotting activity, factor VIII clotting activity, and von Willebrand factor antigen increased with age in both sexes but plasminogen activator inhibitor 1 activity did not. The modest or absent relations between the indexes measured and age are apparently important explanations of the virtual nonexistence of stroke and ischemic heart disease in Kitava.     

Spatio-Temporal Scale Selection in Video Data

This work presents a theory and methodology for simultaneous detection of local spatial and temporal scales in video data. The underlying idea is that if we process video data by spatio-temporal receptive fields at multiple spatial and temporal scales, we would like to generate hypotheses about the spatial extent and the temporal duration of the underlying spatio-temporal image structures that gave rise to the feature responses. For two types of spatio-temporal scale-space representations, (i) a non-causal Gaussian spatio-temporal scale space for offline analysis of pre-recorded video sequences and (ii) a time-causal and time-recursive spatio-temporal scale space for online analysis of real-time video streams, we express sufficient conditions for spatio-temporal feature detectors in terms of spatio-temporal receptive fields to deliver scale-covariant and scale-invariant feature responses. We present an in-depth theoretical analysis of the scale selection properties of eight types of spatio-temporal interest point detectors in terms of either: (i)–(ii) the spatial Laplacian applied to the first- and second-order temporal derivatives, (iii)–(iv) the determinant of the spatial Hessian applied to the first- and second-order temporal derivatives, (v) the determinant of the spatio-temporal Hessian matrix, (vi) the spatio-temporal Laplacian and (vii)–(viii) the first- and second-order temporal derivatives of the determinant of the spatial Hessian matrix. It is shown that seven of these spatio-temporal feature detectors allow for provable scale covariance and scale invariance. Then, we describe a time-causal and time-recursive algorithm for detecting sparse spatio-temporal interest points from video streams and show that it leads to intuitively reasonable results. An experimental quantification of the accuracy of the spatio-temporal scale estimates and the amount of temporal delay obtained from these spatio-temporal interest point detectors is given, showing that: (i) the spatial and temporal scale selection properties predicted by the continuous theory are well preserved in the discrete implementation and (ii) the spatial Laplacian or the determinant of the spatial Hessian applied to the first- and second-order temporal derivatives leads to much shorter temporal delays in a time-causal implementation compared to the determinant of the spatio-temporal Hessian or the first- and second-order temporal derivatives of the determinant of the spatial Hessian matrix.     

Biosensor-based determination of folic acid in fortified food

A newly developed method for the quantification of folic acid in fortified food is presented. An immunoaffinity-based optical biosensor was used to determine folic acid concentration levels in milk powder, infant formula and cereal samples. Accuracy of the method (88–101%) was demonstrated with the analysis of five reference samples. A collaborative precision study, where ten participants at four different laboratories analysed a set of ten samples, resulted in repeatability relative standard deviations of 2–8% and reproducibility relative standard deviations of 4–10%.