In this paper, we propose four new general constructions of LCZ/ZCZ sequence sets based on interleaving technique and affine transformations. A larger family of LCZ/ZCZ sequence sets with longer period are generated by these constructions, which are more flexible among the selection of the alphabet size, the period of the sequences and the length of LCZ/ZCZ, compared with those generated by the known constructions. Especially, two families of the newly constructed sequences can achieve or almost achieve the theoretic bound.

This paper investigates the use of the affine transformation matrix when employing principal component analysis (PCA) to compress the data of 3D animation models. Satisfactory results were achieved for the common 3D models by using PCA because it can simplify several related variables to a few independent main factors, in addition to making the animation identical to the original by using linear combinations. The selection of the principal component factor (also known as the base) is still a subject for further research. Selecting a large number of bases could improve the precision of the animation and reduce distortion for a large data volume. Hence, a formula is required for base selection. This study develops an automatic PCA selection method, which includes the selection of suitable bases and a PCA separately on the three axes to select the number of suitable bases for each axis. PCA is more suitable for animation models for apparent stationary movement. If the original animation model is integrated with transformation movements such as translation, rotation, and scaling (RTS), the resulting animation model will have a greater distortion in the case of the same base vector with regard to apparent stationary movement. This paper is the first to extract the model movement characteristics using the affine transformation matrix and then to compress 3D animation using PCA. The affine transformation matrix can record the changes in the geometric transformation by using 44 matrices. The transformed model can eliminate the influences of geometric transformations with the animation model normalized to a limited space. Subsequently, by using PCA, the most suitable base vector (variance) can be selected more precisely.

Both the Hopfield network and the genetic algorithm are powerful tools for object recognition tasks, e.g., subgraph matching problems. Unfortunately, they both have serious drawbacks. The Hopfield network is very sensitive to its initial state, and it stops at a local minimum if the initial state is not properly given. The genetic algorithm, on the other hand, usually only finds a near-global solution, and it is time-consuming for large-scale problems. In this paper, we propose an integrated scheme of these two methods, while eliminating their drawbacks and keeping their advantages, to solve object recognition problems under affine transformations. Some arrangements and programming strategies are required. First, we use some specialized 2-D genetic algorithm operators to accelerate the convergence. Second, we extract the "seeds" of the solution of the genetic algorithm to serve as the initial state of the Hopfield network. This procedure further improves the efficiency of the system. In addition, we also include several pertinent post matching algorithms for refining the accuracy and robustness. In the examples, the proposed scheme is used to solve some subgraph matching problems with occlusions under affine transformations. As shown by the results, this integrated scheme does outperform many counterpart algorithms in accuracy, efficiency, and stability.

Based on Radon transform, a novel method for registering a periodic (self-referencing) watermark is presented. Although the periodic watermark is widely used as a countermeasure for affine transformation, there is no known efficient method to register it. Experimental results show that the proposed method is effective for registering the watermark from an image that had undergone both affine transformations and severe lossy compression.

This paper describes a novel method of shape matching by means of unification and expansion of local correspondences on the feature points. The method has the ability to simultaneously locate plural similar parts of two-dimensional objects under affine transformation. Furthermore, the method is applicable to the objects partially occluded. Experimental results show that the method yields results that are satisfactory, even for the cases with additions, deletions and local deviations of some feature points.

A method to recognize planar objects undergoing affine transformation is proposed in this paper. The method is based upon wavelet multiscale features and Hopfield neural networks. The feature vector consists of the multiscale wavelet transformed extremal evolution. The evolution contains the information of the contour primitives in a multiscale manner, which can be used to discriminate dominant points, hence a good initial state of the Hopfield network can be obtained. Such good initiation enables the network to converge more efficiently. A wavelet normalization scheme was applied to make our method scale invariant and to reduce the distortion resulting from normalizing the object contours. The Hopfield neural network was employed as a global processing mechanism for feature matching and made our method suitable to recognize planar objects whose shape distortion arising from an affine transformation. The Hopfield network was improved to guarantee unique and more stable matching results. A new matching evaluation scheme, which is computationally efficient, was proposed to evaluate the goodness of matching. Two sets of images, noiseless and noisy industrial tools, undergoing affine transformation were used to test the performance of the proposed method. Experimental results showed that our method is not only effective and robust under affine transformation but also can limit the effect of noises.

A moment-based method is proposed to estimate the illumination change between two images containing affinetransformed objects. The change is linearly modeled with parameters to be estimated by histograms due to its invariance of translation, rotation, and scaling. The parameters can be correctly estimated for an appropriate illumination change by normalizing the moments of the histograms.

Research in very low-bit rate coding has made significant advancements in the past few years. Most recently, the introduction of the MPEG-4 proposal has motivated a wide variety of a approaches aimed at achieving a new level of video compression. In this paper we review progress in VLBV categorized into 3 main areas. (1) Waveform coding, (2) 2D Content-based coding, and (3) Model-based coding. Where appropriate we also described proposals to the MPEG-4 committee in each of these areas.

Hybrid image coding method is one of the most promising methods for efficient coding of moving images. The method makes use of jointly motion-compensated prediction and orthogonal transform like DCT. This type of coding scheme was adopted in several world standards such as H.261 and MPEG in ITU-T and ISO as a basic framework [1], [2]. Most of the work done in motion-compensated prediction has been based on a block matching method. However, when input moving images include complicated motion like rotation or enlargement, it often causes block distortion in decoded images, especially in the case of very low bit-rate image coding. Recently, as one way of solving this problem, some motion-compensated prediction methods based on an affine transform or bilinear transform were developed [3]-[8]. These methods, however, cannot always express the appearance of the motion in the image plane, which is projected plane form 3-D space to a 2-D plane, since the perspective transform is usually assumed. Also, a motion-compensation method using a perspective transform was discussed in Ref, [6]. Since the motion detection method is defined as an extension of the block matching method, it can not always detect motion parameters accurately when compared to gradient-based motion detection. In this paper, we propose a new motion-compensated prediction method for coding of moving images, especially for very low bit-rate image coding such as less than 64 kbit/s. The proposed method is based on a perspective transform and the constraint principle for the temporal and spatial gradients of pixel value, and complicated motion in the image plane including rotation and enlargement based on camera zooming can also be detected theoretically in addition to translational motion. A computer simulation was performed using moving test images, and the resulting predicted images were compared with conventional methods such as the block matching method using the criteria of SNR and entropy. The results showed that SNR and entropy of the proposed method are better than those of conventional methods. Also, the proposed method was applied to very low bit-rate image coding at 16 kbit/s, and was compared with a conventional method, H.261. The resulting SNR and decoded images in the proposed method were better than those of H.261. We conclude that the proposed method is effective as a motion-compensated prediction method.