@article{unal_yezzi_krim_2005, title={Information-theoretic active polygons for unsupervised texture segmentation}, volume={62}, ISSN={["1573-1405"]}, DOI={10.1007/s11263-005-4880-6}, abstractNote={Curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances, hence can not account for higher order nature of the textural characteristics of image regions. In addition, the object delineation by active contour methods, results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases. Polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding. The key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process. This model can robustly capture texture boundaries by way of higher-order statistics of the data and using an information-theoretic measure and with its nature of the ordinary differential equations. This new variational texture segmentation model, is unsupervised since no prior knowledge on the textural properties of image regions is used. Another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles. This is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners.}, number={3}, journal={INTERNATIONAL JOURNAL OF COMPUTER VISION}, author={Unal, G and Yezzi, A and Krim, H}, year={2005}, pages={199–220} }
 @article{unal_krim_yezzi_2002, title={Stochastic differential equations and geometric flows}, volume={11}, ISSN={["1057-7149"]}, DOI={10.1109/TIP.2002.804568}, abstractNote={In previous years, curve evolution, applied to a single contour or to the level sets of an image via partial differential equations, has emerged as an important tool in image processing and computer vision. Curve evolution techniques have been utilized in problems such as image smoothing, segmentation, and shape analysis. We give a local stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a tangential diffusion movement of the particles along the contour. Moreover, assuming that a priori information about the shapes of objects in an image is known, we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise. We also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features, in contrast to the original geometric heat flow which tends to circularize any closed curve.}, number={12}, journal={IEEE TRANSACTIONS ON IMAGE PROCESSING}, author={Unal, G and Krim, H and Yezzi, A}, year={2002}, month={Dec}, pages={1405–1416} }
 @article{hamza_krim_unal_2002, title={Unifying probabilistic and variational estimation}, volume={19}, ISSN={["1053-5888"]}, DOI={10.1109/MSP.2002.1028351}, abstractNote={A maximum a posteriori (MAP) estimator using a Markov or a maximum entropy random field model for a prior distribution may be viewed as a minimizer of a variational problem.Using notions from robust statistics, a variational filter referred to as a Huber gradient descent flow is proposed. It is a result of optimizing a Huber functional subject to some noise constraints and takes a hybrid form of a total variation diffusion for large gradient magnitudes and of a linear diffusion for small gradient magnitudes. Using the gained insight, and as a further extension, we propose an information-theoretic gradient descent flow which is a result of minimizing a functional that is a hybrid between a negentropy variational integral and a total variation. Illustrating examples demonstrate a much improved performance of the approach in the presence of Gaussian and heavy tailed noise. In this article, we present a variational approach to MAP estimation with a more qualitative and tutorial emphasis. The key idea behind this approach is to use geometric insight in helping construct regularizing functionals and avoiding a subjective choice of a prior in MAP estimation. Using tools from robust statistics and information theory, we show that we can extend this strategy and develop two gradient descent flows for image denoising with a demonstrated performance.}, number={5}, journal={IEEE SIGNAL PROCESSING MAGAZINE}, author={Hamza, AB and Krim, H and Unal, GB}, year={2002}, month={Sep}, pages={37–47} }
 @article{unal_cetin_2001, title={Restoration of error-diffused images using projection onto convex sets}, volume={10}, ISSN={["1057-7149"]}, DOI={10.1109/83.974568}, abstractNote={A novel inverse halftoning method is proposed to restore a continuous tone image from a given half-tone image. A set theoretic formulation is used where three sets are defined using the prior information about the problem. A new space-domain projection is introduced assuming the halftoning is performed using error diffusion, and the error diffusion filter kernel is known. The space-domain, frequency-domain, and space-scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution.}, number={12}, journal={IEEE TRANSACTIONS ON IMAGE PROCESSING}, author={Unal, GB and Cetin, AE}, year={2001}, month={Dec}, pages={1836–1841} }
 @article{unal_yardimci_arikan_cetin_2000, title={QR-RLS algorithm for error diffusion of color images}, volume={39}, number={11}, journal={Optical Engineering (Redondo Beach, Calif.)}, author={Unal, G. B. and Yardimci, Y. and Arikan, O. and Cetin, A. E.}, year={2000}, pages={2860–2866} }