This paper presents a novel image edge detection algorithm based on lifting scheme. Image is transformed at dyadic scales based on lifting scheme. A multiresolution edge point is considered if the magnitude of gradien...This paper presents a novel image edge detection algorithm based on lifting scheme. Image is transformed at dyadic scales based on lifting scheme. A multiresolution edge point is considered if the magnitude of gradient attains a local maximum along the gradient direction. Theory and empirical result show that this algorithm is robust. Its time and space complexity is low and its result is precise and reliable.展开更多
A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of ...A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).展开更多
We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-poin...We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-point and odd-pointinterpolating schemes of lower and higher arity belong to this family of schemes. Wealso present tensor product version of generalized and unified families of schemes.Moreover error bounds between limit curves and control polygons of schemes arealso calculated. It has been observed that error bounds decrease when complexityof the scheme decrease and vice versa. Furthermore, error bounds decrease withthe increase of arity of the schemes. We also observe that in general the continuityof interpolating scheme do not increase by increasing complexity and arity of thescheme.展开更多
Many-knot spline interpolating is a class of curves and surfaces fitting method presentedin 1974. Many-knot spline interpolating curves are suitable to computer aided geometric design anddata points interpolation. In ...Many-knot spline interpolating is a class of curves and surfaces fitting method presentedin 1974. Many-knot spline interpolating curves are suitable to computer aided geometric design anddata points interpolation. In this paped, the properties of many-knot spline interpolating curves arediscussed and their applications in font design are considered. The differences between many-knotspline interpolating curves and the curves genoaed by exceeding-lacking adjuStment algorithm aregiven.展开更多
This paper offers a general formula for surface subdivision rules for quad meshes by using 2-D Lagrange interpolating polynomial [1]. We also see that the result obtained is equivalent to the tensor product of (2N + 4...This paper offers a general formula for surface subdivision rules for quad meshes by using 2-D Lagrange interpolating polynomial [1]. We also see that the result obtained is equivalent to the tensor product of (2N + 4)-point n-ary interpolating curve scheme for N ≥ 0 and n ≥ 2. The simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented by L. Kobbelt [2], which can be directly calculated from the proposed formula. Furthermore, some characteristics and applications of the proposed work are also discussed.展开更多
This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any?integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed wor...This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any?integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed work is extended for surface case, which is equivalent to the tensor product of above proposed curve case. These formulas merge several notorious curve/surface schemes. Furthermore, visual performance of the subdivision schemes is also presented.展开更多
文摘This paper presents a novel image edge detection algorithm based on lifting scheme. Image is transformed at dyadic scales based on lifting scheme. A multiresolution edge point is considered if the magnitude of gradient attains a local maximum along the gradient direction. Theory and empirical result show that this algorithm is robust. Its time and space complexity is low and its result is precise and reliable.
文摘A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).
基金The first author was supported by Pakistan Program for Collaborative Research-foreign visit of local faculty member,Higher Education Commission(HEC)PakistanThe second author was supported by Indigenous Ph.D.Scholarship Scheme of HEC PakistanThe third author was supported by NSF of China(No.61073108)
文摘We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-point and odd-pointinterpolating schemes of lower and higher arity belong to this family of schemes. Wealso present tensor product version of generalized and unified families of schemes.Moreover error bounds between limit curves and control polygons of schemes arealso calculated. It has been observed that error bounds decrease when complexityof the scheme decrease and vice versa. Furthermore, error bounds decrease withthe increase of arity of the schemes. We also observe that in general the continuityof interpolating scheme do not increase by increasing complexity and arity of thescheme.
文摘Many-knot spline interpolating is a class of curves and surfaces fitting method presentedin 1974. Many-knot spline interpolating curves are suitable to computer aided geometric design anddata points interpolation. In this paped, the properties of many-knot spline interpolating curves arediscussed and their applications in font design are considered. The differences between many-knotspline interpolating curves and the curves genoaed by exceeding-lacking adjuStment algorithm aregiven.
文摘This paper offers a general formula for surface subdivision rules for quad meshes by using 2-D Lagrange interpolating polynomial [1]. We also see that the result obtained is equivalent to the tensor product of (2N + 4)-point n-ary interpolating curve scheme for N ≥ 0 and n ≥ 2. The simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented by L. Kobbelt [2], which can be directly calculated from the proposed formula. Furthermore, some characteristics and applications of the proposed work are also discussed.
文摘This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any?integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed work is extended for surface case, which is equivalent to the tensor product of above proposed curve case. These formulas merge several notorious curve/surface schemes. Furthermore, visual performance of the subdivision schemes is also presented.
