Convective regularization for optical flow

We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field $v$ we consider the convective acceleration $v_t + \nabla v v$ which describes the acceleration of objects moving according to $v$. Consequently we investigate the suitability of the nonconvex functional $\|v_t + \nabla v v\|^2_{L^2}$ as a regularization term for optical flow. We demonstrate that this term acts as both a spatial and a temporal regularizer and has an intrinsic edge-preserving property. We incorporate it into a contrast invariant and time-regularized variant of the Horn-Schunck functional, prove existence of minimizers and verify experimentally that it addresses some of the problems of basic quadratic models. For the minimization we use an iterative scheme that approximates the original nonlinear problem with a sequence of linear ones. We believe that the convective acceleration may be gainfully introduced in a variety of optical flow models

Optical Flow on Moving Manifolds

Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying image domain. To that end we construct a Riemannian metric that describes the deformation and structure of this evolving surface. The resulting functional can be seen as natural geometric generalization of previous work by Weickert and Schn\"orr (2001) and Lef\`evre and Baillet (2008) for static image domains. In this work we show the existence and wellposedness of the corresponding optical flow problem and derive necessary and sufficient optimality conditions. We demonstrate the functionality of our approach in a series of experiments using both synthetic and real data.Comment: 26 pages, 6 figure

Decomposition of Optical Flow on the Sphere

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are motivated by recent trends in image analysis. In particular we treat $u+v$ decomposition as well as hierarchical decomposition. Helmholtz decomposition of motion fields is obtained as a natural by-product of the chosen numerical method based on vector spherical harmonics. All models are tested on time-lapse microscopy data depicting fluorescently labelled endodermal cells of a zebrafish embryo.Comment: The final publication is available at link.springer.co

Innovating on Well Biofouling Remediation: A Bacteriophage Cocktail Approach

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La grafiosis de los olmos en Austria

Dutch elm disease (DED) has first been recorded in Austria in 1928 and subsequently caused severe damage to elms in this country. In the 1990s studies on the incidence and geographical distribution of Ophiostoma ulmi and the subspecies of O. novo-ulmi in Austria have been initiated. Additionally, efforts were made to identify hybrids between these subspecies. In this paper we present a synthesis of this research and review the history and impact of DED in Austria. By the 1990s only O. novo-ulmi was present in Austria and O. ulmi had already disappeared. Based on its unique colony morphology and its female sterility, one isolate is suspected of being a hybrid or introgressant between O. ulmi and O. novo-ulmi. Both subspecies of O. novo-ulmi were detected in Austria, with ssp. novo-ulmi occurring more frequently than ssp. americana, and their ranges overlap, which suggests that they hybridize in this part of Europe. Examination of seven isolates of O. novo-ulmi for their fertility response as donor to authenticated isolates of O. novo- ulmi and by PCR-RFLP of the cerato-ulmin (cu) gene and colony type (col1) gene have unequivocally shown that genetic recombination occurs between ssp. novo-ulmi and ssp. americana and that Austria forms part of a hybrid zone between O. novo-ulmi ssp. novo-ulmi and O. novo-ulmi ssp. americana.La grafiosis del olmo se detectó por primera vez en Austria en 1928. Posteriormente causó graves daños a los olmos de este país. En la década de 1990 se iniciaron en Austria los estudios sobre la incidencia y la distribución geográfica de Ophiostoma ulmi y de las subespecies de O. novo-ulmi. Igualmente se ha realizado esfuerzos para identificar híbridos entre ambas especies. En este artículo presentamos una síntesis de estas investigaciones y una revisión de la historia y el impacto de la grafiosis en Austria. Hacia 1990 únicamente O. novo-ulmi estaba presente en Austria, habiendo ya desaparecido O. ulmi. Se sospecha, teniendo en cuenta la presencia de una morfología colonial única y de esterilidad femenina, que uno de los aislamientos es un híbrido o el resultado de una introgresión entre O. ulmi y O. novo-ulmi. Ambas subespecies de O. novo-ulmi se han detectado en Austria, siendo más frecuente la ssp. novo-ulmi que la ssp. americana, y existiendo una superposición en su área de distribución, lo que sugiere que se pueden hibridar en esta parte de Europa. El estudio de siete aislamientos de O. novo-ulmi en cuanto a su fertilidad como donantes frente a aislamientos conocidos, y en cuanto a su análisis mediante PCR-RFLP de los genes cerato-ulmina (cu) y tipo de colonia (col1) ha mostrado inequívocamente que existe una recombinación genética entre las subespecies novo-ulmi y americana y que Austria forma parte de una zona de hibridación entre O. novo-ulmi ssp. novo-ulmi y O. novo-ulmi ssp. americana