SMS freeforms for illumination

SMS 3D (simultaneous multiple surfaces in their three-dimensional version) is a well-known design method comprising two freeform surfaces that allow the perfect coupling of two wavefronts with another two. The design algorithm provides a collection of line pairs on both surfaces (called SMS spines), whose three-dimensional shape seems arbitrary at first sight. This paper shows that the shapes of the spines are partially governed by applying the étendue conservation theorem to the biparametric bundle of rays linking the paired spines, which is one lesser known étendue invariants found by Poincaré. The resulting formulae for the spines in three-dimensional space happen to coincide with the conventional étendue formulas of two-dimensional geometry, like for instance, the Hottel formula.

Text segmentation in unconstrained hand-drawings in whiteboard photos

In this paper we present a robust method to detect handwritten text from unconstrained drawings on normal whiteboards. Unlike printed text on documents, free form handwritten text has no pattern in terms of size, orientation and font and it is often mixed with other drawings such as lines and shapes. Unlike handwritings on paper, handwritings on a normal whiteboard cannot be scanned so the detection has to be based on photos. Our work traces straight edges on photos of the whiteboard and builds graph representation of connected components. We use geometric properties such as edge density, graph density, aspect ratio and neighborhood similarity to differentiate handwritten text from other drawings. The experiment results show that our method achieves satisfactory precision and recall. Furthermore, the method is robust and efficient enough to be deployed in a mobile device. This is an important enabler of business applications that support whiteboard-centric visual meetings in enterprise scenarios. © 2012 IEEE.