Digitization often introduces distortions in the form of odd perspective and curved text lines, especially toward the spine region of bound documents, that tamper both the creation of an acceptable digital reproduction of the document and the successful extraction of its textual content using OCR techniques. While already known for traditional acquisition means such as flatbed or planetary scanners, the problem gets even worse with the use of cameras, whose current widespread availability may open new opportunities for librarians and archivists. Dewarping is in charge of handling this kind of problems. This paper proposes a novel model-based dewarping method, aimed at solving some of the shortcomings of existing approaches through the use of a mixture of image processing and numerical analysis tools. The method is based on the construction of a curvilinear grid on each page of the document by means of piecewise polynomial fit and appropriate equipartition of a selection of its curved text lines. We show the method on sample documents and evaluate its impact on successful rate of OCR on a dataset.

We consider Hermitian matrix valued functions depending on three parameters that vary in a bounded surface of $\R^3$ . We study how to detect when such functions have coalescing eigenvalues inside this surface. Our criterion to locate these singularities is based on a construction suggested by Stone in [20]. For generic coalescings, any such singularity is related to a particular accumulation of a certain phase, or lack thereof, as we cover the surface.

Consider a matrix valued function $A(x)\in\R^{m imes n}$, $m\ge n$, smoothly depending on parameters $x\in\Omega\subset \R^2$, where $\Omega$ is simply connected and bounded. We consider a technique to locate parameter values where some of the $q$ dominant ($q\le n$) singular values of $A$ coalesce, in the specific case when $A$ is large and $m> n\gg q$.