Guo-Qin Zheng

A numerically stable fragile watermarking scheme for authenticating 3D models

This paper analyzes the numerically instable problem in the current 3D fragile watermarking schemes. Some existing fragile watermarking schemes apply the floating-point arithmetic to embed the watermarks. However, these schemes fail to work properly due to the numerically instable problem, which is common in the floating-point arithmetic. This paper proposes a numerically stable fragile watermarking scheme. The scheme views the mantissa part of the floating-point number as an unsigned integer and operates on it by the bit XOR operator. Since there is no numerical problem in the bit operation, this scheme is numerically stable. The scheme can control the watermark strength through changing the embedding parameters. This paper further discusses selecting appropriate embedding parameters to achieve good performance in terms of the perceptual invisibility and the ability to detect unauthorized attacks on the 3D models. The experimental results show that the proposed public scheme could detect attacks such as adding noise, adding/deleting faces, inserting/removing vertices, etc. The comparisons with the existing fragile schemes show that this scheme is easier to implement and use.

Using diffusion distances for flexible molecular shape comparison.

BackgroundMany molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.ResultsIn this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.ConclusionsWe illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.

Computing minimum distance between two implicit algebraic surfaces

The minimum distance computation problem between two surfaces is very important in many applications such as robotics, CAD/CAM and computer graphics. Given two implicit algebraic surfaces, a new method based on the offset technique is presented to compute the minimum distance and a pair of points where the minimum distance occurs. The new method also works where there are an implicit algebraic surface and a parametric surface. Quadric surfaces, tori and canal surfaces are used to demonstrate our new method. When the two surfaces are a general quadric surface and a surface which is a cylinder, a cone or an elliptic paraboloid, the new method can produce two bivariate equations where the degrees are lower than those of any existing method.

Surface area estimation of digitized 3D objects using quasi-Monte Carlo methods

A novel and efficient quasi-Monte Carlo method for estimating the surface area of digitized 3D objects in the volumetric representation is presented. It operates directly on the original digitized objects without any surface reconstruction procedure. Based on the Cauchy-Crofton formula from integral geometry, the method estimates the surface area of a volumetric object by counting the number of intersection points between the objects boundary surface and a set of uniformly distributed lines generated with low-discrepancy sequences. Using a clustering technique, we also propose an effective algorithm for computing the intersection of a line with the boundary surface of volumetric objects. A number of digitized objects are used to evaluate the performance of the new method for surface area measurement.

An offset algorithm for polyline curves

Polyline curves which are composed of line segments and arcs are widely used in engineering applications. In this paper, a novel offset algorithm for polyline curves is proposed. The offset algorithm comprises three steps. Firstly, the offsets of all the segments of polyline curves are calculated. Then all the offsets are trimmed or joined to build polyline curves that are called untrimmed offset curves. Finally, a clipping algorithm is applied to the untrimmed offset curves to yield the final results. The offset algorithm can deal with polyline curves that are self-intersection, overlapping or containing small arcs. The new algorithm has been implemented in a commercial system TiOpenCAD 8.0 and its reliability is verified by a great number of examples.

Automatic G1 arc spline interpolation for closed point set

A method for generating an interpolation closed G1 arc spline on a given closed point set is presented. For the odd case, i.e. when the number of the given points is odd, this paper disproves the traditional opinion that there is only one closed G1 arc spline interpolating the given points. In fact, the number of the resultant closed G1 arc splines fulfilling the interpolation condition for the odd case is exactly two. We provide an evaluation method based on the arc length as well such that the choice between those two arc splines is made automatically. For the even case, i.e. when the number of the given points is even, the points are automatically moved based on weight functions such that the interpolation condition for generating closed G1 arc splines is satisfied, and that the adjustment is small. And then, the G1 arc spline is constructed such that the radii of the arcs in the spline are close to each other. Examples are given to illustrate the method.

Line Segment Intersection Testing

A method for accurately determining whether two given line segments intersect is presented. This method uses the standard floating-point arithmetic that conforms to IEEE 754 standard. If three or four ending points of the two given line segments are on a same vertical or horizontal line, the intersection testing result is obtained directly. Otherwise, the ending points and their connections are mapped onto a 3×3 grid, and the intersection testing falls into one of the five testing classes. The intersection testing method is based on our method for floating-point dot product summation, whose error bound is 1ulp. Our method does not have the limitation in the method of Gavrilova and Rokne (2000) that the product of two floating-point numbers is calculated by a twice higher precision floating-point arithmetic than that of the multipliers. Furthermore, this method requires less than one-fifth of the running time used by the method of Gavrilova and Rokne (2000), and our new method for calculating the sign of a sum of n floating-point numbers requires less than one-fifteenth of the running time used by ESSA.

Alternate pattern fill

An algorithm for alternate pattern fill on arbitrary line segments, circular arcs and elliptical arcs is proposed in this paper. The algorithm creates an external loop which is a minimal loop that contains a given point. And then, all loops that delimit the nested regions for the alternate pattern fill inside the external loop are built. The loop detection is based on a new method for searching the leftmost edges. It requires only values of positions, tangent vectors, curvature radii, and the first derivatives of curvature radii at intersection points and areas of circles and ellipses. After all necessary loops are built, the given pattern is filled in the nested loops inside the external loop. Filling the given pattern in this paper is simplified into filling line segment patterns on some parallel lines.

Computing the sign of a dot product sum

A real number usually cannot be exactly represented by a floating-point number in a computer. Namely, a floating-point number frequently stands for any real number in a specific interval. In this paper, we present a method for computing the sign of a dot product sum. Each initial datum that is a floating-point number is considered as an interval. With interval analysis and floating-point summation methods, an explicit formula for calculating the minimal interval of a dot product sum is presented. Error analysis and some examples are provided as well.