We present a novel scheme for digital steganography of point-sampled geometry in the spatial domain. Our algorithm is inspired by the concepts proposed by Cayre and Macq for 3D polygonal models. It employs a principal component analysis (PCA), resulting in a blind approach. We validate our scheme with various model complexities in terms of capacity, complexity, visibility, and security. This scheme is robust against translation, rotation, and scaling operations. It is fast and can achieve high data capacity with insignificant visual distortion in the stego models.

Sampling is important for many applications in research areas such as graphics, vision, and image processing. In this paper, we present a novel stratified sampling algorithm (SSA) for the coiled tubing surface with a given probability density function. The algorithm is developed from the inverse function of the integration for the areas of the coiled tubing surface. We exploit a Hierarchical Allocation Strategy (HAS) to preserve sample stratification when generating any desirable sample numbers. This permits us to reduce variances when applying our algorithm to Monte Carlo Direct Lighting for realistic image generation. We accelerate the sampling process using a segmentation technique in the integration domain. Our algorithm thus runs 324 orders of magnitude faster when using faster SSA algorithm where the order of the magnitude is proportional to the sample numbers. Finally, we employ a parabolic interpolation technique to decrease the average errors occurred for using the segmentation technique. This permits us to produce nearly constant average errors, independent of the sample numbers. The proposed algorithm is novel, efficient in computing and feasible for realistic image generation using Monte Carlo method.