Kernel Learning for Dynamic Texture Synthesis

Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article compares and contrasts members from a general class of regularization techniques, which notably includes ridge regression and principal component regression. We derive an explicit finite-sample risk bound for regularization-based estimators that simultaneously accounts for (i) the structure of the ambient function space, (ii) the regularity of the true regression function, and (iii) the adaptability (or qualification) of the regularization. A simple consequence of this upper bound is that the risk of the regularization-based estimators matches the minimax rate in a variety of settings. The general bound also illustrates how some regularization techniques are more adaptable than others to favorable regularity properties that the true regression function may possess. This, in particular, demonstrates a striking difference between kernel ridge regression and kernel principal component regression. Our theoretical results are supported by numerical experiments.

In this paper, the innovative method for analyzing and synthesizing nonlinear dynamic textures is proposed. To capture nonlinear motion, dynamic textures are modeled by dynamic texture units. The dynamic texture units' parameters are learnt at the same time. We use Daubechies discrete wavelet transform, and different color coding i.e. YCbCr, YUV, and YIQ to get better visual quality and compact representation. This is a more accepted and a highly flexible algorithm. It exploits the spatial, temporal, and chromatic correlations amongst the pixels to get the more compact model parameters. The proposed algorithm is simple, automatic, and it works well on various types of dynamic textures. We have done the testing on various dynamic textures. It reconstructs the dynamic texture sequences with promising visual quality and fewer coefficients. The testing result shows the proposed dynamic system along with Daubechies discrete wavelet transform, and YIQ color coding achieves a higher compact model with an acceptable visual quality than the available LDS (Linear Dynamic System) and Fourier descriptor model. A compact representation for dynamic texture synthesis is very useful for embedded devices, which have a limited memory and computational power, such as tablets, mobile phones, etc.

The Gaussian mixture model (GMM) method is popular and efficient for voice conversion (VC), but it is often subject to overfitting. In this paper, the principal component regression (PCR) method is adopted for the spectral mapping between source speech and target speech, and the numbers of principal components are adjusted properly to prevent the overfitting. Then, in order to better model the nonlinear relationships between the source speech and target speech, the kernel principal component regression (KPCR) method is also proposed. Moreover, a KPCR combined with GMM method is further proposed to improve the accuracy of conversion. In addition, the discontinuity and oversmoothing problems of the traditional GMM method are also addressed. On the one hand, in order to solve the discontinuity problem, the adaptive median filter is adopted to smooth the posterior probabilities. On the other hand, the two mixture components with higher posterior probabilities for each frame are chosen for VC to reduce the oversmoothing problem. Finally, the objective and subjective experiments are carried out, and the results demonstrate that the proposed approach shows greatly better performance than the GMM method. In the objective tests, the proposed method shows lower cepstral distances and higher identification rates than the GMM method. While in the subjective tests, the proposed method obtains higher scores of preference and perceptual quality.

Dynamic texture can be defined as a temporally continuous and infinitely varying stream of images that exhibit certain temporal statistics. Linear dynamic system (LDS) represented by the state-space equation has been proposed to model dynamic texture [12]. LDS can be used to synthesize dynamic texture by sampling the system noise. However, the visual quality of the synthesized dynamic texture using noise-driven LDS is often unsatisfactory. In this paper, we regard the noise-driven LDS as an open-loop control system and analyze its stability through its pole placement. We show that the noise-driven LDS can produce good quality dynamic texture if the LDS is oscillatory. To deal with an LDS not oscillatory, we present a novel approach, called closed-loop LDS (CLDS) where feedback control is introduced into the system. Using the succeeding hidden states as an input reference signal, we design a feedback controller based on the difference between the current state and the reference state. An iterative algorithm is proposed to generate dynamic textures. Experimental results demonstrate that CLDS can produce dynamic texture sequences with promising visual quality.KeywordsUnit CircleVisual QualityHide StateLinear Dynamic SystemTexture SynthesisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The texture is a repetition of a particular structure. Textures classified into static texture and dynamic texture. There are two approaches for synthesising dynamic textures: image‐based approach and physics‐based approach. In the proposed work, the synthesis of different dynamic textures is shown. The physics‐based approach is used to synthesise dynamic texture videos. Different mathematical models are proposed which are suitable to give appropriate motion to the dynamic textures. The raw frames are created, and these frames are further used to synthesise the dynamic textures using physics laws and mathematical formulae. The flexibility of each model is demonstrated. The proposed model has less specificity and less computational complexity. The proposed algorithms are implemented on the graphics processing unit to reduce the overall execution time and time complexity. High‐quality videos are produced, and the evaluation of every frame assures the quality.

We consider the problem of categorizing video sequences of dynamic textures, i.e., nonrigid dynamical objects such as fire, water, steam, flags, etc. This problem is extremely challenging because the shape and appearance of a dynamic texture continuously change as a function of time. State-of-the-art dynamic texture categorization methods have been successful at classifying videos taken from the same viewpoint and scale by using a Linear Dynamical System (LDS) to model each video, and using distances or kernels in the space of LDSs to classify the videos. However, these methods perform poorly when the video sequences are taken under a different viewpoint or scale. In this paper, we propose a novel dynamic texture categorization framework that can handle such changes. We model each video sequence with a collection of LDSs, each one describing a small spatiotemporal patch extracted from the video. This Bag-of-Systems (BoS) representation is analogous to the Bag-of-Features (BoF) representation for object recognition, except that we use LDSs as feature descriptors. This choice poses several technical challenges in adopting the traditional BoF approach. Most notably, the space of LDSs is not euclidean; hence, novel methods for clustering LDSs and computing codewords of LDSs need to be developed. We propose a framework that makes use of nonlinear dimensionality reduction and clustering techniques combined with the Martin distance for LDSs to tackle these issues. Our experiments compare the proposed BoS approach to existing dynamic texture categorization methods and show that it can be used for recognizing dynamic textures in challenging scenarios which could not be handled by existing methods.

The main challenge of dynamic texture synthesis lies in how to maintain spatial and temporal consistency in synthesized videos. The major drawback of existing dynamic texture synthesis models comes from poor treatment of the long-range texture correlation and motion information. To address this problem, we incorporate a new loss term, called the Shifted Gram loss, to capture the structural and long-range correlation of the reference texture video. Furthermore, we introduce a frame sampling strategy to exploit long-period motion across multiple frames. With these two new techniques, the application scope of existing texture synthesis models can be extended. That is, they can synthesize not only homogeneous but also structured dynamic texture patterns. Thorough experimental results are provided to demonstrate that our proposed dynamic texture synthesis model offers state-of-the-art visual performance.

This paper presents a novel framework that aims to complete background holes with still or dynamic textures in a video captured by a fixed or moving camera In our method, background mosaics are constructed based on camera motion estimation to establish the correspondence map between the to-be-filled pixels and the corresponding available or synthesized data obtained/trained from the non-occluded background in neighboring frames. By using a linear dynamic system model for dynamic texture analysis and synthesis, the proposed method can handle the completion of dynamic textured background. After filling the background holes with synthesized background data, we perform Mending-based post-processing on the boundaries of completed background in both the spatial and temporal domains to alleviate the artifacts of ghost shadows and flickers due to the spatio-temporal unsmoothed transitions on the boundaries. Experimental results show that the proposed method can nicely maintain both the spatial and temporal consistency of background after completion.

The objective of this study was to compare the predictions of the protein contents and hardness values by partial least squares regression (PLSR) and principal components regression (PCR) models for bulk samples of Canadian wheat, which were obtained from different locations and crop years. Wheat samples of Canada Western Red Spring (CWRS), Canada Western Hard White Spring (CWHWS), Canada Western Soft White Spring (CWSWS), and Canada Prairie Spring Red (CPSR) classes were obtained from nearby agricultural farms in the main wheat growing locations in the Provinces of Alberta, Saskatchewan, and Manitoba from 2007, 2008, and 2009 crop years. Wheat samples were conditioned to moisture levels of 13, 16, and 19 % (wet basis) and pooled together for developing the regression models. A database of the near-infrared (NIR) hyperspectral image cubes of bulk samples of wheat classes was created in the wavelength region of 960–1,700 nm with 10 nm intervals. Reference protein contents and hardness values were determined using the Dumatherm method and single kernel characterization system (SKCS), respectively. A tenfold cross-validation was used for the ten-factor partial least squares regression (PLSR) and principal components regression (PCR) models for prediction purposes. Prediction performances of regression models were assessed by calculating the estimated mean square errors of prediction (MSEP), standard error of cross-validation (SECV), and correlation coefficient (r). Using the full data set in the protein prediction study, the ten-component PLSR model gave 1.76, 1.33, and 0.68 for the estimated MSEP, SECV, and r, respectively, which were better than the results for the ten-component PCR model (2.02, 1.42, and 0.62, respectively). For the hardness prediction, the estimated MSEP, SECV, and r values were 147.7, 12.15, and 0.82, respectively, for the ten-component PLSR model using the full data set. The PLSR models prediction performances outperformed the PCR models for predicting protein contents and hardness of wheat.

Visible and near-infrared diffuse reflectance spectroscopy has been widely applied in precision agriculture to develop soil property prediction models. This method assumes that residuals of prediction are independently and identically distributed. However, this assumption is violated by spatial dependence common in soil samples collected from agricultural fields, and subsequent prediction models are usually sub-optimal. In this article, the regression-kriging method was used to account for spatial dependence among soil samples and aid in prediction model development. A total of 273 soil samples were collected from an agricultural field in Quitman County, Mississippi. Particle size distribution (clay and sand) and chemical analysis (Ca, K, Mg, Na, P, and Zn) were performed in the laboratory. Soil reflectance spectra were measured with a spectroradiometer (250 to 2500 nm). Soil samples were divided into two groups: 245 samples in the calibration set, and 28 samples in the validation set. The calibration set was first used to develop the principal component regression (PCR) models for each soil property. Semivariance analysis of prediction residuals from PCR revealed strong spatial dependence in Na; medium spatial dependence in Ca, Mg, and sand; weak spatial dependence in K and P; and a pure nugget effect in Zn and clay. Fitted theoretical semivariograms were then used to develop the regression-kriging models. Both the PCR and regression-kriging models were tested with the validation set, and their prediction capability was evaluated by R2 and RMSE (root mean squared error). The results showed that the only two soil properties that could be predicted by the PCR models were Mg (R2 = 0.4 and RMSE = 25.4%) and Ca (R2 = 0.33 and RMSE = 16.6%). On the other hand, the regression-kriging models were able to predict most soil properties with reasonably high R2 (reaching 0.65) and low RMSE. Most impressively, substantial increases of R2 and decreases of RMSE were achieved by the regression-kriging models for Na (R2 = 0.65 and RMSE = 29.0%, compared to R2 = 0.10 and RMSE = 44.4% in the PCR model) and sand (R2 = 0.49 and RMSE = 19.8%, compared to R2 = 0.06 and RMSE = 26.0% in the PCR model). It is anticipated that the proposed method could be integrated into GIS packages for various precision agriculture applications, such as digital soil mapping based on remotely sensed hyperspectral images.

Dynamic textures are sequences of images of moving scenes that show stationarity properties in time. Eg: waves, flame, fountain, etc. Recent attempts at generating, potentially, infinitely long sequences model the dynamic texture as a Linear Dynamic System. This assumes a linear correlation in the input sequence. Most real world sequences however, exhibit nonlinear correlation between frames. In this paper, we propose a technique of generating dynamic textures using a low dimension model that preserves the non-linear correlation. We use nonlinear dimensionality reduction to create an embedding of the input sequence. Using this embedding, a nonlinear mapping is learnt from the embedded space into the image input space. Any input is represented by a linear combination of nonlinear bases functions centered along the manifold in the embedded space. A spline is used to move along the input manifold in this embedded space as a similar manifold is created for the output. The nonlinear mapping learnt on the input is used to map this new manifold into a sequence in the image space. Output sequences, thus created, contain images never present in the original sequence and are very realistic.

Principal component regression (PCR) model is developed, in this study, for predicting and forecasting the abundance of CO2 emission which is the most important greenhouse gas in the atmosphere that contributes to global warming. The model was compared with supervised principal component regression (SPCR) model and was found to have more predictive power than it using the values of Akaike information criterion (AIC) and Swartz information criterion (SIC) of the models.Keywords: Global warming, CO2, Principal component regression (PCR), Supervised principal component regression (SPCR), Akaike information criterion (AIC) and Swartz information criterion (SIC)

This paper focuses on the physically reliable detection of fire, where the multispectral calibration of camera and multispectral-Martin-distance-based fire detection are studied. By regarding the multispectral irradiance sequence of fire as dynamic texture and studying the sequence with the Linear Dynamic System (LDS) model, we represent the sequence with the parameters of the LDS model. The multispectral Martin distance is defined to measure the degree of difference between image sequences. The fire detection method based on the multispectral martin distance realized the combination of the dynamic texture recognition technology and the multispectral-based fire detection. Experiments are conducted on two datasets to validate the effectiveness of our method. The work of this paper made the fire detection results more physically reliable.

This book highlights the estimation of crop yield in Central Gujarat, especially with regard to the development of Multiple Regression Models and Principal Component Regression (PCR) models using climatological parameters as independent variables and crop yield as a dependent variable. It subsequently compares the multiple linear regression (MLR) and PCR results, and discusses the significance of PCR for crop yield estimation. In this context, the book also covers Principal Component Analysis (PCA), a statistical procedure used to reduce a number of correlated variables into a smaller number of uncorrelated variables called principal components (PC). This book will be helpful to the students and researchers, starting their works on climate and agriculture, mainly focussing on estimation models. The flow of chapters takes the readers in a smooth path, in understanding climate and weather and impact of climate change, and gradually proceeds towards downscaling techniques and then finally towards development of principal component regression models and applying the same for the crop yield estimation

Forecasting wine phenolic composition from infrared spectra of grapes extracts and monitoring of fermentations with optimised time-specific prediction models