Akira Kawanaka

Radar imaging of underground pipes by automated estimation of velocity distribution versus depth

A method is presented for enhancing GPR images of underground point reflectors, such as buried pipes, by automated estimation of the velocity distribution versus depth. An x-t radar image is first processed by f-k migration for various propagation velocities v. This process is the well-known velocity analysis by diffraction stacking. An x-t-v data matrix is then constructed from these migrated x-t radar images using different propagation velocities v. Next, we simultaneously extract the hyperbolic apex and estimate the propagation velocity of each hyperbola, using the x-t-v data matrix. Interpolating these estimated discrete propagation velocities along the t-axis, we can derive the propagation velocity distribution versus depth. Extracting the image intensity from the x-t-v data matrix along with the derived propagation velocity distribution yields an enhanced reconstructed image of the underground section. The effectiveness of this method is demonstrated by comparing the results of processing experimental GPR data using the automated x-t-v data matrix method with previous methods. This method automatically reconstructs the enhanced underground section at low computing cost.

Zerotree coding of wavelet coefficients for image data on arbitrarily shaped support

[Summary form only given]. A wavelet coding method for arbitrarily shaped image data, applicable to object-oriented coding of moving pictures, and to the efficient representation of texture data in computer graphics is proposed. The wavelet transform of an arbitrarily shaped image is obtained by applying the symmetrical extension technique at region boundaries and keeping the location of the wavelet coefficient. For entropy coding of the wavelet coefficients, the zerotree coding technique is modified to work with arbitrarily shaped regions by treating missing (outside of the decomposed support) coefficients as insignificant and transmitting only those zerotree symbols which are in the decomposed support. The coding performance of the proposed method for several test images that include a person, a teapot and a necklace is compared to a shape-adaptive DCT and an ordinary DCT method applying low pass extrapolation to the DCT block containing the region boundaries. Experiments show that the proposed method has a better coding efficiency compared to SA-DCT and the ordinary DCT method.

Depth estimation from stereo images using sparsity

In this paper, we propose a new method for correcting the depth image, which was obtained by applying a matching scheme to stereo images and often includes parts with large error, based on the sparsity of depth image. When the depth image is obtained by a stereo matching, a small pixel correspondence error causes large estimation errors in the depth image. Also, original depth image can be considered to have sparsity the same as many natural signals without noise. So we correct the depth image that was obtained by the stereo matching, based on the sparsity of the original depth image. First, the depth image parts with a higher probability of containing large estimation errors are selected as the areas in which the depth has relatively large difference from that which was obtained by applying the median filter to the estimated depth image. Second, the depth image is applied with the inpainting procedure based on the data sparsity [1] as shown in Fig. 1 in which the data of the selected area are treated as being lost. In particular the depth image in a region, which corresponds to an object in 3-D space, is wavelet transformed by SA-DWT (Shape-Adaptive Discrete Wavelet Transform). The smaller wavelet coefficients are truncated to zero with a threshold procedure. With decreasing threshold value, the wavelet transform, smaller coefficient zeroing, and the inverse wavelet transform processes are repeated until the processed depth image is converged. Experiments show that the proposed method is able to remove large errors in the depth image which had been obtained by the stereo matching scheme.

Polygonal mesh data compression based on triangular lattice structuring and wavelet transform

In this paper, we describe a triangular lattice structuring method for 3D polygonal mesh data and a shape-adaptive wavelet transform of the structured geometry and textural data. Efficient representations of a 3D object data has attracted wide attention for transmission and storage of computer graphics data and interactive design in manufacturing. Polygonal mesh data, which consist of connectivity information, geometry data and textural data, are often used for representing a 3D object in many applications. We propose a method for structuring the polygonal mesh data on a triangular lattice plane with expanded nodes. And a shape-adaptive wavelet coding method is applied to the structured geometry data considering the expanded nodes. Experimental results show that the proposed method gives better coding performance than the topologically assisted geometry compression scheme.

Permuting and lifting wavelet coding for structured 3-D geometry data with expanded nodes

One promising method for coding 3-D geometry data is based on the structure processing of a 3-D model on triangle lattice planes, while maintaining connectivity. In the structuring process, each vertex may be assigned to several nodes on the triangular lattice planes. One of the nodes to which a vertex is assigned is selected as a representative node and the others are called expanded nodes. Only geometry data of the vertices at the representative nodes are required for reconstructing the 3-D model. The geometry data at the representative nodes are often separated by expanded nodes on the triangular lattice plane. In this paper we apply a lifting wavelet transform with the permuting process for an expanded node at even locations and the neighboring representative node to reduce the correlations among the separated coordinate values in the lower frequency band. Experimental results for the 3-D model with complex connectivity show the proposed scheme gives better coding performance compared to the usual schemes.

Compression of 3D shape data using SA-WT

A data compression method applying a wavelet transform and hierarchical quantization for geometry data structured by a quadrilateral mesh is proposed. The geometry data is transformed into multi-scale wavelet coefficients of the same number as the original data by applying a shape-adaptive wavelet transform along two axes of the quadrilateral mesh. The wavelet coefficients are entropy coded by an optimal method called combined zero tree quantization, which takes into account dependency of the coefficients at similar positions in each scale, with scalar quantization of the remained coefficients. The performance of the proposed method is evaluated using two metrics based on shape distortion and normal vector distortion of reconstructed geometry data, and the experimental results show that the new method performs remarkably well compared to conventional methods.

Triangular Mesh Geometry Coding with Multiresolution Decomposition Based on Structuring of Surrounding Vertices

In this paper, we propose a new polygonal mesh geometry coding scheme based on a process of structuring by acquiring surrounding vertices of the polygonal mesh one layer at a time. The structuring process begins by selecting the start vertex and proceeding by acquiring surrounding vertices of the polygonal mesh. As a result, we obtain a 2-D structured vertex table. Structured geometry data are generated according to the structured vertices and encoded by a multiresolution decomposition and space frequency quantization coding method. In our proposed scheme, the multiresolution decomposition uses the connectivity of the polygonal mesh. In addition, with a space frequency quantization coding scheme, we can reduce redundancies of decomposed coefficients at similar positions in different components of decomposition level. Experimental results show that the proposed scheme gives better coding performance at lower bit-rates than the usual schemes.

Asymptotic decorrelation of between-scale wavelet coefficients of generalized fractional process

Recent interest on the wavelet transform of digital random signals with long-memory is significantly due to the approximate decorrelation of their wavelet coefficients, which simplifies system identification and estimation. In this paper, we show that for a fairly general model of long-memory across-scale autocovariances of wavelet coefficients converge rapidly to zero, and we determine the rate of converge. The result provides useful groundwork for wavelet-based processing of long-memory random signals.

Multiresolution decomposition for triangular mesh geometry coding based on structuring surrounding vertices

A novel coding method using multiresolution decomposition for triangular mesh is proposed. We have proposed surrounding vertices structuring on a 2-D plane to obtain 2-D structured geometry data. In this paper, non-separable component decomposition is proposed to decompose the structured geometry data in consideration of correlations among neighboring vertices. The structured data are decomposed into four components depending on whether each vertex was located at even or odd positions along the horizontal and vertical axes. And a prediction and update are performed. In the prediction process the predicted value is obtained from the non-processed vertices neighboring to the target vertex in the 3-D space. By repeating the decomposition process for the update component, octave-decomposed coefficients are obtained. The vector SFQ is introduced to remove redundancies among the coefficients at similar positions in different resolution levels. Experiments showed that the proposed method gave better coding performances comparing to conventional coding schemes.

Permuting and Lifting Wavelet Coding for Structured Geometry Data of 3-D Polygonal Mesh

This paper presents a lifting wavelet coding technique with permutation and coefficient modification processes for coding the structured geometry data of 3-D polygonal mesh model. One promising method for coding 3-D geometry data is based on the structure processing of a 3-D model on a triangle lattice plane, while maintaining connectivity. In the structuring process, each vertex may be assigned to several nodes on the triangular lattice plane. One of the nodes to which a vertex is assigned is selected as a representative node and the others are called expanded nodes. Only the geometry data of the vertices at the representative nodes are required for reconstructing the 3-D model. In this paper we apply a lifting wavelet transform with a permutation process for an expanded node at an even location in each decomposition step and the neighboring representative node. This scheme arranges more representative nodes into the lower frequency band. Also many representative nodes separated from the connective expanded nodes are made to adjoin each other in lower frequency bands, and the correlation between the representative nodes will be reduced by the following decomposition process. A process is added to use the modified coefficients obtained from the coefficients of the adjacent representative nodes instead of the original coefficients in the permutation process. This has the effect of restraining increases in the decomposed coefficients with larger magnitude. Some experiments in which the proposed scheme was applied to structured geometry data of a 3-D model with complex connectivity show that the proposed scheme gives better coding performance and the reconstructed models are more faithful to the original in comparison with the usual schemes.