Page segmentation is a key task in document processing, enabling effective extraction of structured information from diverse document types. This paper presents an in-depth analysis of the method proposed by Kise et al., a bottom-up approach using area Voronoi diagrams to identify spatial relationships between document parts. Our work provides a detailed description of the method, emphasizing clarity, reproducibility, and transparency, particularly regarding aspects not fully specified in the original paper. We highlight the impact of the parameter settings and preprocessing steps on the method's performance. Through extensive testing, we demonstrate that the method can handle a wide range of layouts but exhibits notable sensitivity to specific document characteristics, especially in handling complex elements like handwritten text, lists, drop-caps, and tables.
We introduce a novel image segmentation algorithm based on the methodology of approximating solutions to backward stochastic differential equations (BSDEs). The segmentation method repeats the BSDE reconstruction process, with the parameters of these equations changing in subsequent steps. We are interested in a sequence of images driven by BSDE solutions. As the segmentation result, we define the limit of these images. By their nature, stochastic tools, particularly the Monte Carlo method, have high computational complexity. There are concerns about the running time of the proposed method, especially if we are considering a sequence of stochastic solutions. Experimental segmentation results show that it is possible to obtain results quickly and that the algorithm yields excellent results for images with intense noise.
In many applications, planar spline interpolations of scattered data on the sphere are unsatisfactory; spherical splines are desired. Wahba (1981) defined the thin-plate splines on the sphere by analogy with the polynomial splines on the circle and the thin-plate splines in Rd. The thin-plate spline fit to a scattered data set on the sphere is the solution to an empirical risk minimization problem that penalizes the infidelity of the fit to the data as well as its "wiggliness". This latter term is the square of a seminorm penalty based on the Laplace-Beltrami operator. The minimization problem is posed in a reproducing kernel Hilbert space (RKHS) of functions of finite wiggliness, whose reproducing kernel is isotropic and, due to a result by Schoenberg (1942), given by a Legendre series. A closed-form expression (in terms of the polylogarithm) for the kernel was found by Wendelberger (1982) and re-discovered by Beatson and zu Castell (2018). These closed-form expressions make not just spline interpolation but also downstream signal-processing tasks, such as cubature or resolution of inverse problems, more tractable in fields where scattered data and spherical models are common, such as remote sensing, geostatistics, motion planning, graphics, and medical imaging. In this paper, we present a tutorial on spline methods in RKHSs and show how they can be used to interpolate, smooth, and numerically integrate scattered data on the sphere and solve related inverse problems. The accompanying demo compares thin-plate spline interpolation over the sphere with thin-plate splines on an equirectangular projection and natural cubic splines on a one-dimensional latitudinal projection used in greenhouse gas monitoring. Global mean values of the interpolation surfaces are presented as well, to illustrate how this isotropic spherical kernel-which penalizes interpolant wiggliness without concern for application-specific factors like atmospheric winds-affects the computation of global averages.
In this paper, we describe an implementation of the two-phase image segmentation algorithm proposed by Goldstein, Bresson and Osher in [Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction, Journal of Scientific Computing, 2010]. This algorithm partitions the domain of a given 2D image into foreground and background regions, and each pixel of the image is assigned membership to one of these two regions. The underlying assumption for the segmentation model is that the pixel values of the input image can be summarized by two distinct average values, and that the region boundaries are smooth. Accordingly, the model is formulated as an energy functional whose variable is a region membership function that assigns pixels to either region, as originally proposed by Chan and Vese in [Active Contours Without Edges, IEEE Transactions on Image Processing, 2001]. This energy is the sum of image data terms in the regions and a length penalty for region boundaries. Goldstein, Bresson and Osher modify the energy of Chan-Vese so that their new energy can be minimized efficiently using the split Bregman method to produce an equivalent two-phase segmentation. We provide a detailed implementation of this method, and document its performance with several images over a range of algorithm parameters.
