This paper addresses a method for constructing surface representation of 3D structures from a sequence of cross-sectional images. Firstly, we propose cell-boundary representation, which is a generalization of PVP method proposed by Yun and Park, and develop an efficient surface construction algorithm from a cell-boundary. Cell-boundary consists of a set of boundary cells with their 1-voxel configurations, and can compactly describe binary volumetric data. Secondly, to produce external surface from the cell-boundary representation, we define 19 modeling primitives (MP) including volumetric, planar and linear groups. Surface polygons are created from those modeling primitives using a simple table look-up operation. Since a cell-boundary can be obtained using only topological information of neighboring voxels, there is no ambiguity in determining modeling primitives which may arise in PVP method. Since our algorithm has data locality and is very simple to implement, it is very appropriate for parallel processing.

This paper presents a new approach to the recovery of 3-D structure from multiple pairs of images from different viewpoints. Searching for the corresponding points between images, which is common in stereopsis, is avoided. Extracted edges from input images are projected back into 3-D space, and their intersections are calculated directly. Many false intersections may appear, but if we have many pair images, true intersections are extracted by appropriate thresholding. Octree representation of the intersections enables this approach. We consider a way to treat adjacent edge piexels as a line segment rather than as individual points, which differs from previous works and leads to a new algorithm. Experimental results using both synthetic and actual images are also described.

This paper presents a new idea of photometric stereo method which uses 3 point light sources as illumination source. Its intention is to extract the 3-D information of gastric surface. The merit of this method is that it is applicable to the textured and/or specular surfaces, moreover whose environment is too narrow, like gastric surface. The verification of the proposed method was achieved by the theoretical proof and experiment.

This paper presents a new high-speed three-dimensional (3-D) object recognition system based on two-dimensional (2-D) chain code matching. An observed 3-D object is precisely represented by a 2-D chain code sequence from the discrete surface points of the 3-D object, so that any complex objects can be recognized precisely. Moreover, the normalization procedures such as translation, rotation of 3-D objects except scale changes can be performed systematically and regularly regardless of the complexity of the shape of 3-D objects, because almost all the normalization procedures of 3-D objects are included in the 2-D chain code matching procedure. As a result, the additional normalization procedure become only the processing time for scale changes which can be performed easily by normalizing the length of the chain code sequence. In addition, the fast fourier transformation (FFT) is applicable to 2-D chain code matching which calculates cross correlation between an input object and a reference model, so that very fast recognition is performed. In fact, it is demonstrated that the total recognition time of a 3-D ofject is estimated at 5.35 (sec) using the 28.5-MIPS SPARC workstation.

In this paper we propose a new application of Wu's mechanical theorem proving method to reconstruct polyhedra in 3-D space from their projection image. First we set up three groups of equations. The first group is of the geometric relations expressing that vertices are on a plane segment, on a line segment, and forming angle in 3-D space. The second is of those relations on image plane. And the rest is of the relations between the vertices in 3-D space and their correspondence on image plane. Next, we classify all the groups of equations into two sets, a set of hypotheses and a conjecture. We apply this method to seven cases of models. Then, we apply Wu's method to prove that the hypotheses follow the conjecture and obtain pseudodivided remainders of the conjectures, which represent relations of angles or lengths between 3-D space and their projected image. By this method we obtained new geometrical relations for seven cases of models. We also show that, in the region in image plane where corresponding spatial measures cannot reconstructed, leading coefficients of hypotheses polynomials approach to zero. If the vertex of an image angle is in such regions, we cannot calculate its spatial angle by direct manipulation of the hypothesis polynomials and the conjecture polynomial. But we show that by stability analysis of the pseudodivided remainder the spatial angles can be calculated even in those regions.

This paper proposes an efficient design method of three-dimensional (3-D) recursive digital filters for video signal processing via decomposition of magnitude specifications. A given magnitude specification of a 3-D digital filter is decomposed into specifications of 1-D digital filters with three different (horizontal, vertical, and temporal) directions. This decomposition can reduce design problems of 3-D digital filters to design problems of 1-D digital filters, which can be designed with ease by conventional methods. Consequently, design of 3-D digital filters can be efficiently performed without complicated tests for stability and large amount of computations. In order to process video signal in real time, the 1-D digital filters with temporal direction must be causal, which is not the case in horizontal and vertical directions. Since the proposed method can approximate negative magnitude specifications obtained by the decomposition with causal 1-D R filters, the 1-D digital filters with temporal direction can be causal. Therefore the 3-D digital filters designed by the proposed method is suitable for real time video signal processing. The designed 3-D digital filters have a parallel separable structure having high parallelism, regularity and modularity, and thus is suitable for high-speed VLSI implementation.

Multidimensional signal processing has recently been attracting attention in various fields, and has been studied theoretically. TV receives using 3-D (3-Dimensional: horizontal, vertical and temporal) processing, such as IDTV (ImproveD TV), are already available. In addition, television systems with high quality video and mostly with wide-aspect ratio are being studied worldwide. All the proposed systems adopt 3-D signal processing. 3-D processing can fully utilize the transmitted signal, and can take full advantage of the available bandwidth. This results in improved picture quality. This paper reviews the 3-D signal processing used in IDTV and EDTV (EnhanceD TV) in Japan. Video signals are analyzed in the 3-D frequency domain, and 3-D filter design is also studied.