Biorthogonal Wavelet Transforms and Applications Based on Generalized Progressive Catmull-Clark Subdivision with Shape Control.

In recent years, some biorthogonal Catmull-Clark subdivision wavelet transforms constructed via the lifting scheme have been proposed to speed up processing of geometric models. Thanks to the idea of progressive interpolation, the compression qualities and noise-filtering effects have been improved significantly. However, the reconstruction precision fails to be improved further because many model details are removed and the noise-filtering performance decreases greatly while the noise intensity increases gradually. To deal with this dilemma, a unified Catmull-Clark subdivision based biorthogonal wavelet construction with shape control parameters is presented to process 3D models with sharp-feature constraints. By customizing its local orthogonalizing coefficients for different vertex valences of quadrilateral patches, the novel scheme can greatly strengthen the capability of the model's shape control that is vital for data compression, noise-filtering, etc. Combined with the local and in-place lifting operations, the proposed wavelet transform can dramatically decrease the memory consumption and computation complexity. Both theoretical analysis and numerical experiments show that, compared with the state-of-the-art lifting-based solutions, the proposed wavelet transform achieves higher compression ratio, more stable noise-filtering effects and better progressive transmission quality, not only decreasing the Bits/vertex of 3D meshes and improving the PSNR of reconstructed models, but also reducing the time costs of coding and decoding.

Linearly estimating all parameters of affine motion using Radon transform.

Fast and accurate motion estimation takes an important place in many fields of computer vision and image processing. Using Radon transform to compute projections of the images along specified directions is an effective way to show the relationship between the 2D image object and its projections and estimate motions between the images. All existing projection-based motion estimation methods without the use of iteration have a severe defect that only five of the six affine parameters can be estimated. There are some other methods that can estimate the six parameters, but most of them are usually based on a certain iterative framework, which is computationally intensive and sensitively dependent on the initial values. In this paper, a novel method based on Radon transform is proposed to estimate all the six affine parameters directly. The relationship in the projection domain between a pair of images connected by an affine motion is studied and a linear model is established, by which all the six affine parameters can be directively found. The employment of a hierarchical framework can produce more accurate results. The experimental results reveal that the proposed method has a much better performance than the state-of-the-art methods in this field.

Generalized frequency-domain synthetic aperture focusing technique for ultrasonic imaging of irregularly layered objects.

In ultrasonic nondestructive testing (NDT), the phase shift migration (PSM) technique, as a frequency-domain implementation of the synthetic aperture focusing technique (SAFT), can be adopted for imaging of regularly layered objects that are inhomogeneous only in depth but isotropic and homogeneous in the lateral direction. To deal with irregularly layered objects that are anisotropic and inhomogeneous in both the depth and lateral directions, a generalized frequency- domain SAFT, called generalized phase shift migration (GPSM), is proposed in this paper. Compared with PSM, the most significant innovation of GPSM is that the phase shift factor is generalized to handle anisotropic media with lateral velocity variations. The generalization is accomplished by computer programming techniques without modifying the PSM model. In addition, SRFFT (split-radix fast Fourier transform) input/output pruning algorithms are developed and employed in the GPSM algorithm to speed up the image reconstructions. The experiments show that the proposed imaging techniques are capable of reconstructing accurate shapes and interfaces of irregularly layered objects. The computing time of the GPSM algorithm is much less than the time-domain SAFT combined with the ray-tracing technique, which is, at present, the common method used in ultrasonic NDT industry for imaging layered objects. Furthermore, imaging regularly layered objects can be regarded as a special case of the presented technique.

An adaptable-multilayer fractional fourier transform approach for image registration.

a novel adaptable accurate way for calculating Polar FFT and Log-Polar FFT is developed in this paper, named Multilayer Fractional Fourier Transform (MLFFT). MLFFT is a necessary addition to the pseudo-polar FFT for the following reasons: It has lower interpolation errors in both polar and log-polar Fourier transforms; it reaches better accuracy with the nearly same computing complexity as the pseudo-polar FFT; it provides a mechanism to increase the accuracy by increasing the user-defined computing level. This paper demonstrates both MLFFT itself and its advantages theoretically and experimentally. By emphasizing applications of MLFFT in image registration with rotation and scaling, our experiments suggest two major advantages of MLFFT: 1) scaling up to 5 and arbitrary rotation angles, or scales up to 10 without rotation can be recovered by MLFFT while currently the result recovered by the state-of-the-art algorithms is the maximum scaling of 4; 2) No iteration is needed to obtain large rotation and scaling values of images by MLFFT, hence it is more efficient than the pseudopolar-based FFT methods for image registration.

Principal square root of 3-subdivision-based biorthogonal wavelets.

A new efficient biorthogonal wavelet analysis based on the principal square root of subdivision is proposed in the paper by using the lifting scheme. Since the principal square root of subdivision is of the slowest topological refinement among the traditional triangular subdivisions, the multiresolution analysis based on the principal square root of subdivision is more balanced than the existing wavelet analyses on triangular meshes, and accordingly offers more levels of detail for processing polygonal models. In order to optimize the multiresolution analysis process, the new wavelets, no matter whether they are interior or on boundaries, are orthogonalized with the local scaling functions based on a discrete inner product with subdivision masks. Because the wavelet analysis and synthesis algorithms are actually composed of a series of local lifting operations, they can be performed in linear time. The experiments demonstrate the efficiency and stability of the wavelet analysis for both closed and open triangular meshes with principal square root of subdivision connectivity. The principal square root of -subdivision-based biorthogonal wavelets can be used in many applications such as progressive transmission, shape approximation, multiresolution editing and rendering of 3D geometric models.

Interactive approximate rendering of reflections, refractions, and caustics.

Reflections, refractions, and caustics are very important for rendering global illumination images. Although many methods can be applied to generate these effects, the rendering performance is not satisfactory for interactive applications. In this paper, complex ray-object intersections are simplified so that the intersections can be computed on a GPU, and an iterative computing scheme based on the depth buffers is used for correcting the approximate results caused by the simplification. As a result, reflections and refractions of environment maps and nearby geometry can be rendered on a GPU interactively without preprocessing. We can even achieve interactive recursive reflections and refractions by using an object-impostor technique. Moreover, caustic effects caused by reflections and refractions can be rendered by placing the eye at the light. Rendered results prove that our method is sufficiently efficient to render plausible images interactively for many interactive applications.