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In this paper,the important property of convex object morphology addition is proved that F(S,u)=F(A,u)F(B,u) based on integral geometry,then the two objects' morphology operator can be calculated by through the two point sets' Minkowsky addition which have same normal vector.The concept of vector sphere is provided,every point on a sphere has an only normal vector direction.For any vector in Euclid space there exists a unique correspondent point in the sphere, that means the point's normal vector has the... In this paper,the important property of convex object morphology addition is proved that F(S,u)=F(A,u)F(B,u) based on integral geometry,then the two objects' morphology operator can be calculated by through the two point sets' Minkowsky addition which have same normal vector.The concept of vector sphere is provided,every point on a sphere has an only normal vector direction.For any vector in Euclid space there exists a unique correspondent point in the sphere, that means the point's normal vector has the same direction as in Euclid.Correspond every point's normal vector on an object's surface to a sphere which keep their relative position not changed, the morphology addition of two objects can be simplified as the combination of two vector sphere,a computational model is presented,which unifies the morphology addition,subtraction of 3D objects in theory.The morphology addition algorithm of 2D,3D curves and surfaces is also provided and the application of the 2D,3D curves and surfaces morphology operators is given such as sweep surface modeling,font composition and non rigid body motion interpolation. 从积分几何中的概念出发,证明了凸体形态和运算的一个重要性质: F( S,u)= F( A,u) F( B,u),从而将两物体的形态和归结为法矢相同的点集的形态和,并提出法矢球的概念,将物体表面各点的法矢顺序对应至球,即得到该物体的唯一法矢球表示,通过对法矢球的合并,则得到两物体的形态运算结果,在理论上统一了二维、三维实体的形态运算,并给出二维、三维曲线、曲面的具体形态算法.此外还给出曲线、曲面形态算法的具体应用,如扫成曲面造型、字型合成、非刚体运动的广义内插等. A new method of Chinese or English font derivation based on morphologic operator is proposed. The difference kinds style font can be generated through calculating the Minkowski operator. The principle of this method is also proved and the morphologic addition algorithms for two polygons and Beizer's curves with circle are provided. The experiments show that this method can generate multiple style, high quality font with simple computation. 针对传统汉字字形衍生方法的不足 ,提出了一种全新的基于形态算子的汉字字形衍生方法 .通过对字体不同广义形态运算 ,选择不同的结构元 ,可产生不同的衍生汉字字形 .对多面体及Beizer曲线与圆曲线的形态算法进行了详细讨论 .实验证明运用该方法生成的汉字质量好、自动化程度高 ,可用于三维字体生成 The growth of osteoma is soakage.Osteoma' boundary organ reflect the biological behavior of osteoma.Therefore,it's important to study the fractal characteristics of osteoma boundary.However,there was lack of quantitative parameters depicting these characteristics in the past.With regard to the osteoma of soakage growth,the prognosis is different because of various degree of soakage.It is necessary to use the characteristic parameter in order to reflect soakage growth degree of osteoma.Thus,the fractal characteristics... The growth of osteoma is soakage.Osteoma' boundary organ reflect the biological behavior of osteoma.Therefore,it's important to study the fractal characteristics of osteoma boundary.However,there was lack of quantitative parameters depicting these characteristics in the past.With regard to the osteoma of soakage growth,the prognosis is different because of various degree of soakage.It is necessary to use the characteristic parameter in order to reflect soakage growth degree of osteoma.Thus,the fractal characteristics of osteoma boundary is discussed in this paper. Our results show that fractal dimension can preferably reflect the soakage growth of osteoma' boundary organ. It is a robust characteristic parameter in describing different pathological changes degree of osteoma and prognosis. This provides a new useful approach for lucubrate of osteoma. 由于骨肿瘤呈浸润性生长 ,肿瘤的周边组织反映了肿瘤的生物学行为 ,因此对骨肿瘤边界的研究是非常有意义的 ,但是以往的研究中缺乏描述这些特征的定量指标 ,而同属浸润性生长的肿瘤 ,由于浸润程度不同 ,预后也不同 .因此肿瘤诊断中 ,急需要用一个特征量来反映肿瘤组织生长的浸润程度 .通过骨肿瘤边界的分形特性研究表明 ,用形态算法获得的分形维数 ,能较好地反映骨肿瘤边缘组织的浸润性生长 ,因此它是描述骨肿瘤不同病变程度及预后情况的鲁棒性的特征参数 ,从而为骨肿瘤的深入研究开辟了新的途径 .
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