The theory of the 2-D Wold decomposition of homogeneous random fields is effective in image and video analysis, synthesis, and modeling. However, a robust and computationally efficient decomposition algorithm is needed for use of the theory in practical applications. This paper presents a spectral 3-D Wold decomposition algorithm for homogeneous and near homogeneous random fields. The algorithm relies on the intrinsic fundamental-harmonic relationship among Fourier spectral peaks to identify harmonic frequencies, and uses a Hough transformation to detect spectral evanescent components. A local variance based procedure is developed to determine the spectral peak support. Compared to the two other existing methods for Wold decompositions, global thresholding and maximum-likelihood parameter estimation, this algorithm is more robust and flexible for the large variety of natural images, as well as computationally more efficient than the maximum-likelihood method.

An algorithm for simultaneous detection, segmentation, and characterization of spatiotemporal periodicity is presented. The use of periodicity templates is proposed to localize and characterize temporal activities. The templates not only indicate the presence and location of a periodic event, but also give an accurate quantitative periodicity measure. Hence, they can be used as a new means of periodicity representation. The proposed algorithm can also be considered as a "periodicity filter", a low-level model of periodicity perception. The algorithm is computationally simple, and shown to be more robust than optical flow based techniques in the presence of noise. A variety of real-world examples are used to demonstrate the performance of the algorithm.

One of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems. In applications such as database retrieval, it is important that image features used in pattern comparison provide good measures of image perceptual similarities. We present an image model with a new set of features that address the challenge of perceptual similarity. The model is based on the 2D Wold decomposition of homogeneous random fields. The three resulting mutually orthogonal subfields have perceptual properties which can be described as "periodicity," "directionality," and "randomness," approximating what are indicated to be the three most important dimensions of human texture perception. The method presented improves upon earlier Wold-based models in its tolerance to a variety of local inhomogeneities which arise in natural textures and its invariance under image transformation such as rotation. An image retrieval algorithm based on the new texture model is presented. Different types of image features are aggregated for similarity comparison by using a Bayesian probabilistic approach. The, effectiveness of the Wold model at retrieving perceptually similar natural textures is demonstrated in comparison to that of two other well-known pattern recognition methods. The Wold model appears to offer a perceptually more satisfying measure of pattern similarity while exceeding the performance of these other methods by traditional pattern recognition criteria. Examples of natural scene Wold texture modeling are also presented.

The problem of measuring perceptual similarity between images is addressed using a new image model based on the Weld decomposition. The model permits separate treatment of image components which correspond approximately to periodicity, directionality, and randomness. The authors compare its performance in an image search application to two other methods-one based on shift-invariant principle components and one based on a multiscale simultaneous autoregressive model. When textured images are ordered by distances between their Wold components, the results appear to be much closer to the human perception of similarity. The authors discuss how decoupling the three components can increase flexibility for measuring image similarity and can save computation, permitting the "quickest" matches when the features are the most perceptually "salient".>

One of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems. In applications such as image retrieval, if is important that features used by the system in pattern comparison provide good measures of "perceptual similarity". The authors present a new set of features and an image model based on the three mutually orthogonal components produced by the 2-D Wold decomposition of random fields. These components have visual properties which approximate the three most important perceptual dimensions of human texture perception. The method presented here is different from the existing Wold-based models in that it tolerates certain local inhomogeneities which arise in natural textures and reduces computation for comparison of patterns subjected to transformations such as rotation. An image retrieval algorithm based on the new texture model is presented. The effectiveness of the new Wold features for retrieving perceptually similar natural textures is demonstrated by comparing it to that of other well-known pattern recognition methods. The Wold model appears to offer a perceptually more satisfying measure of pattern similarity.

The Brodatz Album has become the de facto standard for evaluating texture algorithms, with hundreds of studies having been applied to small sets of its images. The authors compare two powerful recognition algorithms, principal components analysis and multiscale autoregressive models, by evaluating them on a 999-image database derived from the entire Brodatz Album. The variety of homogeneous and nonhomogeneous images studied is thus nearly an order of magnitude larger than has been compared before, giving one snapshot of the state of the art in real-time texture recognition.>