Surface mosaics

This paper considers the problem of placing mosaic tiles on a surface to produce a surface mosaic. We assume that the user specifies a mesh model, the size of the tiles and the amount of grout, and optionally, a few control vectors at key locations on the surface indicating the preferred tile orientation at these points. From these inputs, we place equal-sized rectangular tiles over the mesh such as to almost cover it, with controlled orientation. The alignment of the tiles follows a vector field which is interpolated over the surface from the control vectors, and also forced into alignment with any sharp creases, open boundaries, and boundaries between regions of different colors. Our method efficiently solves the problem by posing it as one of globally optimizing a spring-like energy in the Manhattan metric, using overlapping local parameterizations.We demonstrate the effectiveness of our algorithm with various examples

圆组填充算法驱动的平面马赛克模拟

为了生成不规则嵌片排列紧凑的马赛克图案,提出一种基于圆组排列的平面马赛克模拟方法.首先借助嵌片多边形的直骨架得到一组逼近嵌片轮廓的圆;然后以圆半径的平方为权值,在平面上生成关于圆组的Power图,使每组圆各自对应一个Power区域;最后采用松弛法,将圆组在其对应Power区域内尽可能增长到最大.通过不断迭代生成Power图和放大圆组,最后得到嵌片紧凑排列的结果.实验结果表明,该方法得到的马赛克图案有较高的覆盖率,能适应不同嵌片,具有较强的鲁棒性和灵活性.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104);;中央高校基本科研业务费专项基金(20720150002

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

A CD21 low phenotype, with no evidence of autoantibodies to complement proteins, is consistent with a poor prognosis in CLL.

B-cell chronic lymphocytic leukemia (CLL) is characterized by differential BCR signaling and autoimmune complications. Complement modulates B-cell function via C3d and CD21 cross-linked to the B-cell receptor (BCR). We hypothesized that CD21 contributes to BCR signaling and participates in the autoimmunity associated with CLL. We analyzed CD21 expression on 106 CLL patient samples and matched serum from 50 patients for the presence of soluble CD21 and autoantibodies to CR2, CR1, MCP and FH. CD21 expression on CLL B-cells was significantly lower than that expressed on B-cells from age-matched controls (P < 0.0001) and was inversely correlated with soluble CD21 (r2 = –0.41). We found no evidence of autoantibody to any complement regulator. Low CD21 expression correlated to prognostic subsets of CLL patients, i.e. cases with unmutated IGHV genes (P = 0.0006), high CD38 (P = 0.02) and high ZAP70 expression (P = 0.0017). Low CD21 expression was inversely correlated to the levels of phosphotyrosine induced in CLL cells following BCR ligation with αIgM (r2=–0.21). Importantly, lower CD21 expression was also predictive for reduced overall survival (P = 0.005; HR = 2.7). In conclusion, we showed that reduced expression of CD21 on CLL B-cells appears functionally relevant and was associated with poor clinical outcomes

Plato's cube and the natural geometry of fragmentation

Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra -- shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural 2D fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In 3D the Platonic attractor is dominant: remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.Comment: main: 6 pages, 6 figures, supplementary: 18 pages, 12 figure