Kris Popat and Rosalind W. Picard. Cluster-based probability model applied to image restoration and compression. In ICASSP-9J: 199 International Conference on Acoustics, Speech, and Signal Processing, pages 381-384, Adelaide, Australia, April 1994. IEEE.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(likelihood) often results by setting 2 to be slightly larger than the sample Gm,d variance; see [95, Appendix B] for a possible explanation. The GLA was the real work horse algorithm for most of our earlier work in applying mixture models to texture and image processing applications [96, 97, 95]. Later, an improvement was gener ally obtained in all applications by following the GLA with a few iterations of the computationally more expensive expectation maximization (EM) algorithm (to be described in Section 2.6) but 10 In the clustering literature, this algorithm has come to be known ....

Kris Popat and Rosalind W. Picard. Cluster-based probability model applied to image restoration and compression. In ICASSP-9J: 199 International Conference on Acoustics, Speech, and Signal Processing, pages 381-384, Adelaide, Australia, April 1994. IEEE.

....and bitstream consistency. The ML and MAP approaches do not apply directly to the non linear problem of enhancement restoration of compressed images. These approaches requires more powerful and ad hoc constraints for the non linear problem of enhancement or restoration of compressed images. In [32], a ML based solution is proposed by using mixture of Gaussians and clustering analysis. In [53] an optimization method is proposed using the MAP approach for transform based compression. In this approach the estimate of g is given by: g = argmax g L(g j I) 3.4) where L( is the log ....

Kris Popat and Rosalind W. Picard. Cluster-Based Probability Model Applied to Image Restoration and Compression. M.I.T. Technical Report of Media Laboratory Perceptual Computing Group, April 1994.

....Hornegger and Niemann [2] use parameterized mixtures of multivariate Gaussian distributions including a feature transform. This modeling has been shown to be appropriate for point features but cannot be assumed for more general local characteristics. Another possibility is to use kernel functions [5], which typically allow to generalize from training samples, without representing the training samples well. Histogramming, which we have chosen for the presentation of the density function, represents the training samples very well. In the context of histogramming, generalization capability can ....

K. Popat and R.W. Picard. Cluster--based probability model applied to image restoration and compression. In ICASSP, 1994.

.... component of the translation (rep2 resented by the size oe of the object) called the pose s = oe; R) p(M jo n ; s) 2) Representation of p(M jo n ; s) The probability density can be represented in various ways such as by means of a mixture of multivariate Gaussians [5] or kernel estimator [14, 10]. In this paper we use multidimensional histograms. The following shortly discusses why these histograms can be estimated reliably. The six dimensional histograms used in the following contain about 5000 different cells which have to be estimated. In order to obtain a reliable estimate the number ....

K. Popat and R.W. Picard. Cluster--based probability model applied to image restoration and compression. In ICASSP, 1994.

....investigated primarily for the sole objective of improved compression, although Gorman [1] and Wesel et al. 28] have examined such a method for the joint goal. Another is to use a classification scheme such as Stone s generalized nearest neighbors [29] clustered nearest neighbors [30] 31] [32], or Kohonen s learning VQ (LVQ) 5] 6] to classify, and then report the selected nearest neighbor (which implies the class) as the compressed reproduction. A slight modification of this approach (incorporating a centroid step) can yield reasonable compression. Both the independent and the ....

....complexity suggests the use of a tree structured estimator. One such estimator is a tree structured vector quantizer that uses a simple Euclidean nearest neighbor encoder. We note that the use of VQ for pdf estimation is not new; it has been explored by Xie et al. 30] Popat and Picard [32], and Nobel [24] and the use of tree structured methods for classification has been investigated in [13] 17] 19] 39] 40] 41] We construct the TSVQ from empirical distributions of the training data used to design the Bayes VQ. The estimate of the posterior probability is subsequently ....

K. Popat and R. W. Picard, "Cluster-based probability model applied to image restoration and compression", in PICASSP, Adelaide, Australia, April 1994, vol. 5, pp. 381--384.

....fm k ; k = 1; Kg and the pmf can thus be obtained by estimating the proportion c k of data population in each cluster. In this paper, we are only dealing with the continuous pdf which has been successfully applied in applications like classifier design [28] image restoration and compression [20, 21], and etc. Traditionally and statistically, the pdf is constructed by locating a Gaussian kernel at each observed datum, e.g. the fixed width kernel density estimator (FKDE) and the adaptive kernel density estimator (AKDE) Although the FKDE, which constructs a density by placing fixed width ....

....of an FKDE, it does not reduce the high cost incurred in computation and memory storage commonly required in an FKDE. To overcome the problem of high cost in computation and memory storage, a (clustered) radial basis function (RBF) based kernel density estimator, named RBF network, can be used [14, 20, 21]. The RBF network uses a reduced number of (radial basis) kernels, with each kernel being representative of a cluster of training data, to approximate the unknown density function. This method is often referred as mixture (Gaussian) modeling [23] The RBF networks are also widely used in ....

[Article contains additional citation context not shown here]

K. Popat and R.W. Picard. Cluster-based probability model applied to image restoration and compression. To appear in Proc. ICASSP, Adelaide, Australia, April 1994.

....be assumed for more general local image measurements. The other principal possibility is a non parametric estimator for the probability density function. In the context of high dimensional density functions essentially two methods can be applied: histogramming and kernel function estimates [Popat and Picard, 1994]. The main advantage of histogramming is that the training samples are well represented. This property is desirable in our context since we aim to show that the proposed statistical object representation provides a reliable and discriminant means for the recognition of a large number of objects. ....

Popat, K. and Picard, R. (1994). Cluster--based probability model applied to image restoration and compression. In IEEE Conference on Acoustics, Speech and Signal Processing, Adeline, Australia. also M.I.T. Media Laboratory TR 253.

....coding allows us to freely specify any statistical model. The remaining constraint is that the statistical model may be conditioned only on preceding pixels in the chosen ordering. The conditioning structure of the statistical model we consider is patterned after the grayscale extension [10] of the causal neighborhood context model originally proposed in [7] for binary images. Speci cally, for every pixel location in the sequence, a set of nearby but strictly preceding pixel locations is speci ed as a conditioning context. We consider the simplest case, wherein the pixels are encoded ....

K. Popat and R. W. Picard. Cluster-based probability model applied to image restoration and compression. In ICASSP-94: 1994 International Conference on Acoustics, Speech, and Signal Processing, pages 381-384, Adelaide, Australia, April 1994. IEEE.

....using large neighborhoods. These difficulties can be traced to the fact that the number of possible values (states) of the neighborhood increases exponentially with neighborhood size. In previous papers we proposed a particular type of probability model that mitigates some of these difficulties[1, 2]. The proposed model used clustering to summarize relevant information in the training data, and exploited the smoothness of the underlying probability law to effectively interpolate probability between conditioning states. When applied to lossless image compression, the technique allowed ....

....of x, and let N denote their union. Assume that fN j g are disjoint, so that each provides distinct contextual information about x. Since the neighborhoods are small, reliable estimates of p(xjN j ) are readily obtained in a variety of ways, for example by using the cluster based probability model[2]. We therefore assume that such reliable estimates are available. We wish to estimate p(xjN ) by combining the small neighborhood conditional PMF estimates in a manner consistent with the principles set forth in Sections 1 and 2. To this end, we define a measure of agreement by summing the ....

Kris Popat and Rosalind W. Picard. Cluster-based probability model applied to image restoration and compression. In ICASSP-94: 1994 International Conference on Acoustics, Speech, and Signal Processing, Adelaide, Australia, April 1994. IEEE. To appear.

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K. Popat and R. Picard, "Cluster-based probability model applied to image restoration and compression," Perceptual Computing Group Technical Report #TR 233, M.I.T. Media Laboratory, 1993.

....there are difficulties with large neighborhoods. The difficulties can be traced to the fact that the number of possible values (states) of the neighborhood increases exponentially with neighborhood size. In previous papers we proposed a probability model that mitigates some of these difficulties[1, 2]. The model used clustering to summarize relevant information in the training data, and exploited the smoothness of the underlying probability law to effectively interpolate probability between conditioning states. When applied to lossless image compression, the technique allowed processing with ....

....of x, and let N denote their union. Assume that fN j g are disjoint, so that each provides distinct contextual information about x. Since the neighborhoods are small, reliable estimates of p(xjN j ) are readily obtained in a variety of ways, for example by using the cluster based probability model[2]. We therefore assume that such reliable estimates are available. We wish to estimate p(xjN ) by combining the small neighborhood conditional PMF estimates in a manner consistent with the principles set forth in Sections 1 and 2. To this end, we define a measure of agreement by summing the ....

Kris Popat and Rosalind W. Picard. Cluster-based probability model applied to image restoration and compression. In ICASSP-94: 1994 International Con5 ference on Acoustics, Speech, and Signal Processing, Adelaide, Australia, April 1994. IEEE.

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