Computing oriented texture fields

The first step is the analysis of oriented texture consists of the extraction of an orientation field. The orientation field is comprised of the angle and coherence images, which describe at each point the dominant local orientation and degree of anisotropy, respectively. A new algorithm for computing the orientation field for a flow-like texture is presented. The basic idea behind the algorithm is to use an oriented filter, namely the gradient of Gaussian, and perform manipulations on the resulting gradient vector field. The most important aspect of the new algorithm is that it is provably optimal in estimating the local orientation of an oriented texture. An added strength of the algorithm is that it is simpler and has a better signal-to-noise ratio than previous approaches, because it employs fewer derivative operations. We also propose a new measure of coherence, which works better than previous measures. The estimates for orientation and coherence are related to measures in the statistical theory of directional data. We advocate the use of the angle and coherence images as intrinsic images. An analysis of oriented textures will require the computation of these intrinsic images as a first step. In this sense, the computation of the orientation field, resulting in the intrinsic images, is indispensible in the analysis of oriented textures. We provide results from several experiments to indicate the usefulness of the angle and coherence intrinsic images. These results show that the notion of scale plays an important role in the interpretation of textures. Further, measures defined on these intrinsic images are useful for the inspection of surfaces.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29428/1/0000509.pd

Provably scale-covariant networks from oriented quasi quadrature measures in cascade

This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and it is shown that the resulting representation allows for provable scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.Comment: 12 pages, 3 figures, 1 tabl

Dynamic texture recognition using time-causal and time-recursive spatio-temporal receptive fields

This work presents a first evaluation of using spatio-temporal receptive fields from a recently proposed time-causal spatio-temporal scale-space framework as primitives for video analysis. We propose a new family of video descriptors based on regional statistics of spatio-temporal receptive field responses and evaluate this approach on the problem of dynamic texture recognition. Our approach generalises a previously used method, based on joint histograms of receptive field responses, from the spatial to the spatio-temporal domain and from object recognition to dynamic texture recognition. The time-recursive formulation enables computationally efficient time-causal recognition. The experimental evaluation demonstrates competitive performance compared to state-of-the-art. Especially, it is shown that binary versions of our dynamic texture descriptors achieve improved performance compared to a large range of similar methods using different primitives either handcrafted or learned from data. Further, our qualitative and quantitative investigation into parameter choices and the use of different sets of receptive fields highlights the robustness and flexibility of our approach. Together, these results support the descriptive power of this family of time-causal spatio-temporal receptive fields, validate our approach for dynamic texture recognition and point towards the possibility of designing a range of video analysis methods based on these new time-causal spatio-temporal primitives.Comment: 29 pages, 16 figure

Maxwell's Theory of Solid Angle and the Construction of Knotted Fields

We provide a systematic description of the solid angle function as a means of constructing a knotted field for any curve or link in $\mathbb{R}^3$. This is a purely geometric construction in which all of the properties of the entire knotted field derive from the geometry of the curve, and from projective and spherical geometry. We emphasise a fundamental homotopy formula as unifying different formulae for computing the solid angle. The solid angle induces a natural framing of the curve, which we show is related to its writhe and use to characterise the local structure in a neighborhood of the knot. Finally, we discuss computational implementation of the formulae derived, with C code provided, and give illustrations for how the solid angle may be used to give explicit constructions of knotted scroll waves in excitable media and knotted director fields around disclination lines in nematic liquid crystals.Comment: 20 pages, 9 figure

Dilated Spatial Generative Adversarial Networks for Ergodic Image Generation

Generative models have recently received renewed attention as a result of adversarial learning. Generative adversarial networks consist of samples generation model and a discrimination model able to distinguish between genuine and synthetic samples. In combination with convolutional (for the discriminator) and de-convolutional (for the generator) layers, they are particularly suitable for image generation, especially of natural scenes. However, the presence of fully connected layers adds global dependencies in the generated images. This may lead to high and global variations in the generated sample for small local variations in the input noise. In this work we propose to use architec-tures based on fully convolutional networks (including among others dilated layers), architectures specifically designed to generate globally ergodic images, that is images without global dependencies. Conducted experiments reveal that these architectures are well suited for generating natural textures such as geologic structures

A Phase Field Model for Continuous Clustering on Vector Fields

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.