Discriminant analysis of solar bright points and faculae I. Classification method and center-to-limb distribution

While photospheric magnetic elements appear mainly as Bright Points (BPs) at the disk center and as faculae near the limb, high-resolution images reveal the coexistence of BPs and faculae over a range of heliocentric angles. This is not explained by a "hot wall" effect through vertical flux tubes, and suggests that the transition from BPs to faculae needs to be quantitatively investigated. To achieve this, we made the first recorded attempt to discriminate BPs and faculae, using a statistical classification approach based on Linear Discriminant Analysis(LDA). This paper gives a detailed description of our method, and shows its application on high-resolution images of active regions to retrieve a center-to-limb distribution of BPs and faculae. Bright "magnetic" features were detected at various disk positions by a segmentation algorithm using simultaneous G-band and continuum information. By using a selected sample of those features to represent BPs and faculae, suitable photometric parameters were identified in order to carry out LDA. We thus obtained a Center-to-Limb Variation (CLV) of the relative number of BPs and faculae, revealing the predominance of faculae at all disk positions except close to disk center (mu > 0.9). Although the present dataset suffers from limited statistics, our results are consistent with other observations of BPs and faculae at various disk positions. The retrieved CLV indicates that at high resolution, faculae are an essential constituent of active regions all across the solar disk. We speculate that the faculae near disk center as well as the BPs away from disk center are associated with inclined fields

Discriminant analysis of solar bright points and faculae II. Contrast and morphology analysis

Taken at a high spatial resolution of 0.1 arcsec, Bright Points (BPs) are found to coexist with faculae in images and the latter are often resolved as adjacent striations. Understanding the properties of these different features is fundamental to carrying out proxy magnetometry. To shed light on the relationship between BPs and faculae, we studied them separately after the application of a classification method, developed and described in a previous paper) on active region images at various heliocentric angles. In this Paper, we explore different aspects of the photometric properties of BPs and faculae, namely their G-band contrast profiles, their peak contrast in G-band and continuum, as well as morphological parameters. We find that: (1) the width of the contrast profiles of the classified BPs and faculae are consistent with studies of disk center BPs at and limb faculae, which indirectly confirms the validity of our classification, (2) the profiles of limb faculae are limbward skewed on average, while near disk center they exhibit both centerward and limbward skewnesses due to the distribution of orientations of the faculae, (3) the relation between the peak contrasts of BPs and faculae and their apparent area discloses a trend reminiscent of magnetogram studies. The skewness of facular profiles provides a novel constraint for 3D MHD models of faculae. As suggested by the asymmetry and orientation of their contrast profiles, faculae near disk center could be induced by inclined fields, while apparent BPs near the limb seem to be in fact small faculae misidentified. The apparent area of BPs and faculae could be possibly exploited for proxy magnetometry

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

Multi-texture image segmentation

Visual perception of images is closely related to the recognition of the different texture areas within an image. Identifying the boundaries of these regions is an important step in image analysis and image understanding. This thesis presents supervised and unsupervised methods which allow an efficient segmentation of the texture regions within multi-texture images. The features used by the methods are based on a measure of the fractal dimension of surfaces in several directions, which allows the transformation of the image into a set of feature images, however no direct measurement of the fractal dimension is made. Using this set of features, supervised and unsupervised, statistical processing schemes are presented which produce low classification error rates. Natural texture images are examined with particular application to the analysis of sonar images of the seabed. A number of processes based on fractal models for texture synthesis are also presented. These are used to produce realistic images of natural textures, again with particular reference to sonar images of the seabed, and which show the importance of phase and directionality in our perception of texture. A further extension is shown to give possible uses for image coding and object identification