A Lattice Approach to Image Segmentation

After a formal definition of segmentation as the largest partition of the space according to a criterion σ and a function f, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 8), that identifies segmentation with the connections that are based on connective criteria. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria. The soundness of the approach is demonstrated by listing a series of segmentation techniques. One considers first the cases when the segmentation under study does not involve initial seeds. Various modes of regularity are discussed, which all derive from Lipschitz functions. A second category of examples involves the presence of seeds around which the partition of the space is organized. An overall proposition shows that these examples are a matter for the central theorem. Watershed and jump connection based segmentations illustrate this type of situation. The third and last category of examples deals with cases when the segmentation occurs in an indirect space, such as an histogram, and is then projected back on the actual space under study. The relationships between filtering and segmentation are then investigated. A theoretical chapter introduces and studies the two notions of a pulse opening and of a connected operator. The conditions under which a family of pulse openings can yield a connected filter are clarified. The ability of segmentations to generate pyramids, or hierarchies, is analyzed. A distinction is made between weak hierarchies where the partitions increase when going up in the pyramid, and the strong hierarchies where the various levels are structured as semi-groups, and particularly as granulometric semi-groups. The last section is based on one example, and goes back over the controversy about “lattice” versus “functional” optimization. The problem is now tackled via a case of colour segmentation, where the saturation serves as a cursor between luminance and hue. The emphasis is put on the difficulty of grouping the various necessary optimizations into a single one.     

双参数Bézier曲线的升二次扩展

本文以二次Bernstein基函数为例,首次提出了含双参数基函数的新扩展——αβQ—Bern-stein基函数,此类基函数具有新的特点,即基函数的扩展次数一次性升高两次,且包含了二次多项式和带一个参数的三次多项式基函数的所有性质。基于这组基函数定义了αβQ—Bézier曲线,该曲线也含有参数,具有形状可调性,当α与β取某些值时曲线能达到C4连续或在某个端点处C0连续。最后与含两个参数的升一次Bézier曲线进行比较,该曲线具有调节范围广、灵活性更强的优势。     

Distribution in orientation axis of thin film grown by pulsed laser deposition

Orientations of LaNiO₃ (LNO) and Pb(Zr_0.52Ti_0.48)TiO₃ (PZT) films deposited by laser ablation were evaluated using X-ray diffraction. (001)-oriented PZT and LNO films were achieved under optimized deposition conditions. Pole-figure measurements of both LNO and PZT films showed that (001) out-of-plan orientation was affected by plume direction. It was found that the (001) axes of both LNO and PZT films at locations away from the plume center were significantly tilted. The incline angle of tilt increases with the distance away from the center of the plume. The films grown in columnar structures and the column axis coincided with the crystalline orientation. Polarization of the PZT film was slightly affected by the difference in orientation tilt angles of the film investigated.     

曲面片的GC~2连续性

利用微分几何知识给出了一个保证曲面片二阶几何连续(GC~2)的条件。所给出的方法同样适用于公共交界曲线正好是曲面渐近线这种特殊情况。     

C3连续的单位四元数插值样条曲线

目的 构造一类C³连续的单位四元数插值样条曲线,证明它的插值性和连续性,并把它应用于刚体关键帧动画设计中。方法 利用R³空间中插值样条曲线的5次多项式调配函数的累和形式构造了S³空间中单位四元数插值样条曲线,它不仅能精确通过一系列给定的方向,而且能生成C³连续的朝向曲线。结果 与Nielson的单位四元数均匀B样条插值曲线的迭代构造方法相比,所提方法避免了为获取四元数B样条曲线控制顶点对非线性方程组迭代求解的过程,提高了运算效率;与单位四元数代数三角混合插值样条曲线的构造方法（Su方法）相比,所提方法只用到多项式基,运算速度更快。本例中创建关键帧动画所需的时间与Nielson方法和Su方法相比平均下降了73%和33%。而且,相比前两种方法,所提方法产生的四元数曲线连续性更高,由C²连续提高到C³连续,这意味着动画中刚体的朝向变化更加自然。结论 仿真结果表明,本文方法对刚体关键帧动画设计是有效的,对实时性和流畅性要求高的动画设计场合尤为适用。     

Calculation of the concentration profile of copper in the TiN/CoSi<Subscript>2</Subscript>/Si system during thermal heating

The results of the calculation of concentration profiles of copper in the system Cu/TiN/CoSi@2/Si-substrate under thermal heating to 600°C are presented. Possible diffusion mechanisms of Cu in the TiN and CoSi₂ films and bulk Si are considered.     

Constrained approximation of rational Bézier curves based on a matrix expression of its end points continuity condition

For high order interpolations at both end points of two rational Bézier curves, we introduce the concept of C^(v,u)-continuity and give a matrix expression of a necessary and sufficient condition for satisfying it. Then we propose three new algorithms, in a unified approach, for the degree reduction of Bézier curves, approximating rational Bézier curves by Bézier curves and the degree reduction of rational Bézier curves respectively; all are in L₂ norm and C^(v,u)-continuity is satisfied. The algorithms for the first and second problems can get the best approximation results, and for the third one, resorting to the steepest descent method in numerical optimization obtains a series of degree reduced curves iteratively with decreasing approximation errors. Compared to some well-known algorithms for the degree reduction of rational Bézier curves, such as the uniformizing weights algorithm, canceling the best linear common divisor algorithm and shifted Chebyshev polynomials algorithm, the new one presented here can give a better approximation error, do multiple degrees of reduction at a time and preserve high order interpolations at both end points.     

基于三角网格的ternary插值细分法

本文针对规则三角网格,首先提出了一种基于插值3~(1/3)细分法的ternary插值曲面细分法,极限曲面可达C1连续。为使得细分法生成的曲面形状可调,本文进而研究了带参数的ternary插值曲面细分法的构造问题,分析了细分法的连续性。     

关于完全图K_n的{P_4,C_4}-分解

讨论了完全图Kn分解成四个顶点的路和圈的存在性,给出完全图Kn存在{P4,C4}-强制分解的充要条件是n≥5且n≠6.以及完全图Kn存在{P4,C4}-分解的充要条件是n≥4.