Kyungsuk Pyun

Lloyd clustering of Gauss mixture models for image compression and classification

Abstract Gauss mixtures have gained popularity in statistics and statistical signal processing applications for a variety of reasons, including their ability to well approximate a large class of interesting densities and the availability of algorithms such as the Baum–Welch or expectation-maximization (EM) algorithm for constructing the models based on observed data. We here consider a quantization approach to Gauss mixture design based on the information theoretic view of Gaussian sources as a “worst case” for robust signal compression. Results in high-rate quantization theory suggest distortion measures suitable for Lloyd clustering of Gaussian components based on a training set of data. The approach provides a Gauss mixture model and an associated Gauss mixture vector quantizer which is locally robust. We describe the quantizer mismatch distortion and its relation to other distortion measures including the traditional squared error, the Kullback–Leibler (relative entropy) and minimum discrimination information, and the log-likehood distortions. The resulting Lloyd clustering algorithm is demonstrated by applications to image vector quantization, texture classification, and North Atlantic pipeline image classification.

Image Segmentation Using Hidden Markov Gauss Mixture Models

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

Automatic object segmentation in images with low depth of field

The paper describes an automatic object segmentation algorithm for images with low depth of field (DOF). The low DOF images are segmented into two regions, namely, focused objects and defocused background. A local variance image field (LVIF) can represent the pixel-wise spatial distribution of the high-frequency components in the image. However, applying a thresholding method to the LVIF for segmentation often yields blob-like errors in both focused and defocused regions. To eliminate these errors, a block-wise MRF (Markov random field) image model is employed for maximum a posteriori (MAP) segmentation. After the block-wise MAP segmentation, the image blocks in the object boundary are divided into smaller blocks. Then, they are reassigned to one of the neighboring objects through the watershed algorithm, which eventually yields a pixel-level segmentation. Experimental results show that the proposed method yields more accurate segmentation than the multiresolution wavelet-based segmentation method.

Texture classification based on multiple Gauss mixture vector quantizers

We propose a texture classification method using multiple Gauss mixture vector quantizers (GMVQ). We designed a separate model codebook or Gauss mixture for each texture using the generalized Lloyd algorithm with a minimum discrimination information (MDI) distortion based on a training data set. The multi-codebook structure of the GMVQ classifier is an extension to images of the isolated utterance speech recognizer of J.E. Shore and D. Burton (see Proc. Int. Conf. Acoust., Speech, and Sig. Processing, IEEE82Ch.1746-7, p.907-10, 1982). We applied the algorithm to the Brodatz texture database and showed it to be competitive in performance in comparison to other texture classifiers. Its low complexity implementation and real-time operation make the approach suitable for content-based image retrieval.

Robust image classification based on a non-causal hidden Markov Gauss mixture model

We propose a novel image classification method using a non-causal hidden Markov Gauss mixture model (HMGMM) We apply supervised learning assuming that the observation probability distribution given each class can be estimated using Gauss mixture vector quantization (GMVQ) designed using the generalized Lloyd algorithm with a minimum discrimination information (MDI) distortion. The maximum a posteriori (MAP) hidden states in an Ising model are estimated by a stochastic EM algorithm. We demonstrate that HMGMM obtains better classification than several popular methods, including CART, LVQ, causal HMM, and multiresolution HMM, in terms of Bayes risk and the spatial homogeneity of the classified objects. A heuristic solution for the number of clusters achieves a robust image classification.

Image classification using GMM with context information and with a solution of singular covariance problem

Summary form only given. Taking the average of feature vectors from the center and neighboring blocks to a block being coded is proposed as a method of considering context information in block classification. The algorithm has the advantage of low complexity. Gauss mixture models (GMM) are adopted to extract features from image blocks, including an algorithm to handle singular covariance matrices. Two different distortion measures are used; namely log-likelihood quadratic discrimination analysis (QDA) and a dimension-compensated distortion measure defined by dividing the QDA distortion by the corresponding cells dimension. Aerial images were used to train and test. Experimental results show that the proposed algorithm not only improves the classification performance, but also provides a solution to the singular covariance problem.

A Robust Hidden Markov Gauss Mixture Vector Quantizer for a Noisy Source

Noise is ubiquitous in real life and changes image acquisition, communication, and processing characteristics in an uncontrolled manner. Gaussian noise and Salt and Pepper noise, in particular, are prevalent in noisy communication channels, camera and scanner sensors, and medical MRI images. It is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they are quite sensitive to image noise. We propose a modified HMGMM procedure specifically designed to improve performance in the presence of noise. The key feature of the proposed procedure is the adjustment of covariance matrices in Gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion (MDI). In adjusting covariance matrices, we expand or shrink their elements based on the noisy image. While most results reported in the literature assume a particular noise type, we propose a framework without assuming particular noise characteristics. Without denoising the corrupted source, we apply our method directly to the segmentation of noisy sources. We apply the proposed procedure to the segmentation of aerial images with Salt and Pepper noise and with independent Gaussian noise, and we compare our results with those of the median filter restoration method and the blind deconvolution-based method, respectively. We show that our procedure has better performance than image restoration-based techniques and closely matches to the performance of HMGMM for clean images in terms of both visual segmentation results and error rate.

Cost-Effective Hidden Markov Model-Based Image Segmentation

Image segmentation is an important preprocessing step in a sophisticated and complex image processing algorithm. In segmenting real-world images, the cost of misclassification could depend on the true class. For example, in a two-class (negative or positive class) problem, the cost of misclassifying positive to negative class could not be equal to that of misclassifying negative to positive class. However, existing algorithms do not take into account the unequal misclassification cost. In this letter, motivated by recent advances in machine learning theory, we introduce a procedure to minimize the misclassification cost with class-dependent cost. The procedure assumes the hidden Markov model (HMM) which has been popularly used for image segmentation in recent years. We represent all feasible HMM-based segmenters (or classifiers) as a set of points in the receiver operating characteristic (ROC) space. Then, the optimal segmenter (or classifier) is found by computing the tangential point between the iso-cost line with given slope and the convex hull of the feasible set in the ROC space. We illustrate the procedure by segmenting aerial images with different selection of misclassification costs.

Hidden Markov multiresolution texture segmentation using complex wavelets

In block-based statistical texture segmentation approaches, modeling the global dependency between blocks as well as local statistics within a block is important for segmentation performance. A hidden Markov model (HMM) can be combined with a hidden Markov tree (HMT) to form an HMM-HMT model, which captures both global and local properties. Unfortunately, the real wavelet transform, on which the model is based, is not shift-invariant, which degrades the accuracy of the model. Further, its usual implementation uses a single block size, which does not take full advantage of the multiresolution property of wavelets. The HMM-HMT model is modified to use the shift-invariant complex wavelet transform. We also propose a maximum likelihood multiresolution segmentation algorithm, which handles several blocks sizes at once. Global dependencies between blocks are captured through the HMM, while the local statistics are modeled by the complex wavelet HMTs. This method is compared with other models for several test images to demonstrate its competitive performance, especially at small block sizes.

A covariance adjustment method in compressed domain for noisy image segmentation

Noise is ubiquitous in real life and changes image acquisition and processing characteristics in an uncontrolled manner. Highly sophisticated image processing algorithms developed for clean images often malfunction when they are used for noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they have also proved to be quite sensitive to uncontrolled noise in test images. To resolve this difficulty, we propose a modified procedure to adjust covariance matrix estimates of test images. We shrink (or expand) the covariance matrix estimates of the noisy image to make them consistent with those in the codebooks. Note that the covariance matrices in the codebooks are those of the noiseless image. The novelty of this paper is that our method is equivalent to adjusting the covariance matrices of codebooks for noiseless images to be consistent wit those of noisy test images without retraining. The adjusted covariance matrices shrink (or expand) the covariance matrix estimates in the codebooks to minimize the overall minimum discrimination information distortion between test images and codebooks. To illustrate the proposed procedure, we apply it to segmenting aerial images with salt and pepper noise and with Gaussian noise. We compare our method with the median filter restoration method and the blind deconvolution method and show that our procedure has better performance than these image-restoration-based techniques in terms of both visual segmentation results and error rate. Further, we find that the suggested procedure performs almost as well as the HMGMM for clean images, which is the benchmark in comparison.