Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Color-based surface reflectance separation for scene illumination estimation and rendering

Given the importance of color processing in computer vision and computer graphics, estimating and rendering illumination spectral reflectance of image scenes is important to advance the capability of a large class of applications such as scene reconstruction, rendering, surface segmentation, object recognition, and reflectance estimation. Consequently, this dissertation proposes effective methods for reflection components separation and rendering in single scene images. Based on the dichromatic reflectance model, a novel decomposition technique, named the Mean-Shift Decomposition (MSD) method, is introduced to separate the specular from diffuse reflectance components. This technique provides a direct access to surface shape information through diffuse shading pixel isolation. More importantly, this process does not require any local color segmentation process, which differs from the traditional methods that operate by aggregating color information along each image plane. ^ Exploiting the merits of the MSD method, a scene illumination rendering technique is designed to estimate the relative contributing specular reflectance attributes of a scene image. The image feature subset targeted provides a direct access to the surface illumination information, while a newly introduced efficient rendering method reshapes the dynamic range distribution of the specular reflectance components over each image color channel. This image enhancement technique renders the scene illumination reflection effectively without altering the scene’s surface diffuse attributes contributing to realistic rendering effects. ^ As an ancillary contribution, an effective color constancy algorithm based on the dichromatic reflectance model was also developed. This algorithm selects image highlights in order to extract the prominent surface reflectance that reproduces the exact illumination chromaticity. This evaluation is presented using a novel voting scheme technique based on histogram analysis. ^ In each of the three main contributions, empirical evaluations were performed on synthetic and real-world image scenes taken from three different color image datasets. The experimental results show over 90% accuracy in illumination estimation contributing to near real world illumination rendering effects. ^

Monetary cost -efficient query distribution in ISDN -connected heterogeneous databases

Current technology permits connecting local networks via high-bandwidth telephone lines. Central coordinator nodes may use Intelligent Networks to manage data flow over dialed data lines, e.g. ISDN, and to establish connections between LANs. This dissertation focuses on cost minimization and on establishing operational policies for query distribution over heterogeneous, geographically distributed databases. Based on our study of query distribution strategies, public network tariff policies, and database interface standards we propose methods for communication cost estimation, strategies for the reduction of bandwidth allocation, and guidelines for central to node communication protocols. Our conclusion is that dialed data lines offer a cost effective alternative for the implementation of distributed database query systems, and that existing commercial software may be adapted to support query processing in heterogeneous distributed database systems. ^