Tanya Matskewich

Optimizing subpixel rendering using a perceptual metric

— ClearType is a subpixel-rendering method designed to improve the perceived quality of text. The method renders text at subpixel resolution and then applies a one-dimensional symmetric mean-preserving filter to reduce color artifacts. This paper describes a computational method and experimental tests to assess user preferences for different filter parameters. The computational method uses a physical display simulation and a perceptual metric that includes a model of human spatial and chromatic sensitivity. The method predicts experimentally measured preferences for filters for a range of characters, fonts, and displays.

Prediction of preferred ClearType filters using the S-CIELAB metric

The appearance of rendered text is a compromise between the designers intent and the display capabilities. The ClearType rendering method is designed to enhance rendered text by exploiting the subpixel resolution available on color displays. ClearType represents the high-resolution font outline at the full subpixel resolution of the display and then filters the image to enhance contrast and reduce color artifacts. The filter choice influences text appearance, and people have clear preferences between the renderings with different filters. In this paper, we predict these preferences using S-CIELAB, a spatial extension to the perceptual color metric CIELAB. We calculate the S-CIELAB difference between designed and rendered fonts for various filters. We compare the size of these differences with preference data obtained from individual subjects.

A comparison of invariant energies for free-form surface construction

We derive several energy formulations, including Kirchhoff-Love plate energy, firstorder energy and jerk energy. These formulations are based on a new paradigm for free-form surface over arbitrary quadrilateral meshes. The present work briefly recalls the underlying principles of the energy formulation, then considers the various behaviors and resulting surfaces through examples. Each energy term is used separately, or energy terms are combined, to obtain the samples.

MDS for a Smooth Boundary

To construct higher order approximations/interpolations, one also needs to handle smooth boundaries without reducing them to polygonal lines! This chapter deals with such constructions: planar meshes with a smooth global boundary (like the mesh shown in Fig. 5.1). The bilinear in-plane parameterisation is no longer sufficient at the boundary. However, we construct a global in-plane parameterisation in such a way that the local templates are changed only for the boundary vertices and for inner edges adjacent to the boundary.

MDS: Quadrilateral Meshes and Polygonal Boundary

The following mesh limitations are always supposed to be satisfied: the mesh consists of strictly convex quadrilaterals. Every mesh element is a convex quadrilateral and the angle between any two sequential edges is strictly less than π, any inner edge has at most one boundary vertex, boundary vertices have valence 2 (a corner vertex) or 3 (see Fig. 3.1a, b), the situation shown in Fig. 3.1c is not allowed.

G 1 -Smooth Surfaces

The construction of the MDS (defined in Sect. 1.2.4.1) is based on the analysis of the smoothness conditions between adjacent patches. The current chapter contains the formal definitions of G1- and C1-smoothness and presents the general theoretical results of the vertex enclosure problem, which are closely connected to the analysis of the local structure of the MDS. In addition, the present chapter provides some important definitions and notations related to the general flow of the solution and to the analysis of the MDS for the different kinds of “additional” constraints (such as boundary conditions).

Conclusions and Further Research

Our original question: given an unstructured quadrilateral mesh, find an optimal G1 or C1 assembly of Bezier patches based on the mesh, that interpolates the vertices of this mesh, has been completely solved up to cubic C1 boundaries. Rigorous proofs show that for n ≥ 5 there is always a solution. One can also show that the case n = 4 has a solution provided we respect some conditions on the mesh. All the proofs are constructive and have been implemented for the examples we gave.