@conference {
	title = {Optimal Filtering of Digital Binary Images Corrupted by Union/Intersection Noise},
	author = {Sidiropoulos, N D., Baras, John S., Berenstein, Carlos A.},
	year = {1992},
	month = {12/1992},
	abstract = {We model digital binary image data as realizations of a uniformly bounded discrete random set (or discrete random set, for short), a mathematical object which can be directly defined on a finite lattice. We consider the problem of estimating realizations of discrete random sets distorted by a degradation process which can be described by a union/intersection noise model. We start by providing some theoretical justification of the popularity of certain Morphological filters, namely Morphological openings, closings, unions of openings, and intersections of closings. In particular, we prove that if the signal is {\textquotedblleft}smooth{\textquotedblright}, then these filters are optimal (in the sense of providing the MAP estimate of the signal) under reasonable worst-case statistical scenarios. Then we consider a class of filters which arises quite naturally from the set-theoretic analysis of optimal filters. We call this the class of mask filters. We consider both fixed and adaptive mask filters~and derive explicit formulas for the optimal mask filter under quite general assumptions on the signal and the degradation process.},
	address = {Tucson, Arizona},
	booktitle = { The 31st IEEE Conference on Decision and Control},
	pages = {pp. 3287-3292},
	organization = {Westin La Paloma}
}
@conference {
	title = {Optimal Morphological Filters for Discrete Random Sets under a  Union or Intersection Noise},
	author = {Sidiropoulos, N D., Baras, John S., Berenstein, Carlos A.},
	year = {1992},
	month = {11/1992},
	abstract = {We consider the problem of optimal binary image restoration under a union or intersection noise model. Union noise is well suited to model random clutter (obscuration), whereas intersection noise is a good model for random sampling. Our approach is random set-theoretic, i.e. digital images are viewed as realizations of a uniformly bounded discrete random set. First we provide statistical proofs of some "folk theorems{\textquotedblright} of Morphological filtering. In particular, we prove that, under some reasonable worst-case statistical scenarios, Morphological openings, closings, unions of openings, and intersections of closings, can be viewed as MAP estimators of the signal based on the noisy observation. Then we propose a "generic{\textquotedblright} procedure for the design of optimal Morphological filters for independent union or intersection noise.},
	address = {Boston, Massachusetts},
	booktitle = {The SPIE Conference on Visual Communication \& Image Processing},
	pages = {pp. 402-413}
}
@conference {
	title = {The Parametric Wavelet Maxima Representation},
	author = {Berman, Zeev., Baras, John S., Berenstein, Carlos A.},
	year = {1992},
	month = {10/1992},
	abstract = {A general signal description, called an inherently bounded Adaptive Quasi Linear Representation (AQLR), motivated by two important examples, namely, the wavelet maxima representation, and the wavelet zero-crossings representation, is introduced. This paper presents a new reconstruction scheme based on the minimization of an appropriate cost function. The convergence of two described algorithms is guaranteed for all inherently bounded AQLR. As a consequence, we describe possible modifications in the basic multiscale maxima representations.},
	address = {Victoria, British Columbia, Canada},
	booktitle = {IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis},
	pages = {pp. 59-62}
}
@conference {
	title = {Discrete Random Sets: An Inverse Problem, Plus Tools for the Statistical Inference of the Discrete Boolean Model},
	author = {Sidiropoulos, N D., Baras, John S., Berenstein, Carlos A.},
	year = {1992},
	month = {07/1992},
	abstract = {We consider digital binary images as a realization~of a bounded discrete random set, a mathematical object which can be defined directly on a finite lattice. In this setting, we show that it is possible to move between two equivalent probabilistic model specifications. We formulate a restricted version of the discrete-case analog of a Boolean random set model, obtain it{\textquoteright}~probability mass function. and employ some methods of Morphological image analysis to derive tools for its statistical inference.},
	address = {San Diego, California},
	booktitle = {SPIE Conference on Image Algebra and Morphological Image Processing III},
	pages = {pp. 32-43}
}
@conference {
	title = {Optimal Mask Filtering of Discrete Random Sets under a Union/Intersection Noise Model},
	author = {Sidiropoulos, N D., Baras, John S., Berenstein, Carlos A.},
	year = {1992},
	month = {03/1992},
	abstract = {We consider the problem of estimating realizations of highly nonstationary Discrete Random Sets, distorted by a degradation process which can be described by a union/intersection model. We start by presenting some important structural results concerning the probabilistic description of Discrete Random Sets defined on a finite lattice. Then we propose a family of filters which can be viewed as lattice operators, and, for each degradation model, derive the optimal filter by means of minimizing a suitable fidelity criterion.},
	address = {Princeton, New Jersey},
	booktitle = {Twenty-Sixth Annual Conference on Information Sciences and Systems},
	pages = {pp. 313-318},
	organization = {Princeton University}
}
