Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.

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https://hdl.handle.net/11693/13870

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Open Access
Structural analysis of pole assignment and stabilization in dynamic systems
(Bilkent University, 1989) Şefik, Ayla; Sezer, Erol
Motivated by the need for qualitative investigation of general system properties such as controllability, obser\^bility, existence of fixed modes, etc. as the complement of the quantitative approach in analysis, especially of large-scale systems, the problems of pole assignability and stabilizability are considered from the structural point of view. The study is based on the definition of a generic property as a property that holds for almost all values of the nonzero system parameters. Structured matrices and digraphs are used for system description. Both problems are first formulated in an algebraic setting and then translated to a structural framework by means of several graph-theoretic results which give sufficient conditions for solvability, in terms of the existence of particular cycle families in the digraph. Following a similar approach, a graphical investigation of structural observability is presented. Lastly, genericity of several results are reconsidered in the light of these graphical characterizations.
Open Access
Motion artifact reduction techniques in magnetic resonance imaging
(Bilkent University, 1991) Atalar, Ergin; Onural, Levent
It is shown that the expansion/shrinkage and rotational motions of the body cause phase and amplitude distortions and non-rectangular sampling over the A:-domain. If these distortions are not compensated then the reconstructed image will suffer from ''the motion artifact'. The mathematical relation between motion and motion artifact is given. If the motion of the body is known, it is possible to obtain motion artifact free images. The motion is estimated either by using the information in the acquired data or by direct measurement. These estimates and the relation between motion and artifact are used to compensate the phase and amplitude distortions. Using the non-rectangular samples over the ¿-domain the rectangular samples are obtain by the aid of the singular value decomposition method. And finally, the inverse Fourier transform of these calculated samples gives the motion artifact free image. The proposed method is tested by simulations. For the estimation of the motion, two methods are proposed and tested. The first method is an iterative image reconstruction method. The second one uses the navigator echoes to obtain the amount of motion.
Open Access
Decentralized blocking zeros in the control of large scale systems
(Bilkent University, 1992) Ünyelioğlu, Konur Alp; Özgüler, A. Bülent
lu lliis lliesi.s, a luuiiber ot syiithe.sis problems i'or linear. ninc-invariauL, iiiiite-cliuieiiSioiial sysiems are adclres.se(l. It i.s sliown that tlie lu'w concejU of (l·.': m inili zed blocking zeros \s as fmidaineiital to controller .synthesis problems for large scale systems as the concept of decentralized fixed modes. The main problems considered are (i) decentralized stabilization problem, (ii) decentralized strong stabilization problem, and (iii) decentralized concurrent stabilization problem. 7'he dtcenIralized siabUizaiion problem is a fairly well-understood controller synthesis problem for which many synthesis methods exist. Here, we give a new .synthesis procedure via a proper stable fractional approach and focus our attention on the generic solvability and characitnzalion of all solutions. The decenlralized strong .stabilization problem is the problem of stabilizing a .systeni using stable local controllers. In this problem, the .set of decentralized blocking zeros play an essential role and it turns out that the problem has a solution in case tlie poles and the real nonnegative decentralized blocking zeros have parity interlacing property. In the more general problem of decentralized stabilization problem with minimum number of unstable controller poles, it is shown tliat this minimum number is determined by the nuiid.H-»r of odd distributions of plant poles among the real nonnegative decentralized blocking zeros. The decentralized concurrent stabilization problem is a special type of simultaneous stabilization problem using a decentralized controller. Tliis problem is of interest, since many large scale synthesis problems turn out to be its special cases. A complete solution to decentralized concurrent stabilization problem is obtained, where again the decentralized blocking zeros play a central role. Three problems that have receiviHİ wide atteiuion in tlie literature of large scale .systems: stabilization o f composite systems using locally :>tabilizing subsystem controllers, stabilization uf composite system.^ na the slabilization o f mam diagonal transfer matrices, and rcliablt decentralized siabilizaiion problem are solved by a specialization of oiir main result on decentralized concurrent stabilization problem.
Open Access
Digital beamforming techniques and VLSI circuits for medical ultrasound imaging
(Bilkent University, 1992) Karaman, Mustafa; Köymen, Hayrettin
For phased array medical ultrasound imaging, digital beamforming techniques and VLSI circuits are studied to form a fully digital receive front-end hardware. To increase the timing accuracy in beamforming, a computationally efficient upsampling schme is examined. A digital beamforming method based on receive focusing at the raster focal points is proposed. The sector images of the resolution phantom, reconstructed from the phased array experimental data by beamforming at the radial and raster focal points, are presented for comparison of the image resolution performance of the two beamforming schemes. For adaptive beamforming, a phase aberration correction technique with very low computational complexity is described. Image quality performance of the technique is examined by digitally processing the non-aberrated and aberrated phased array experimental data sets of an ultrasound resolution phantom. VLSI circuits and their implementations for the proposed techniques are presented.
Open Access
Performance analysis of an asynchronous transfer mode multiplexer with Markov modulated inputs
(Bilkent University, 1993) Akar, Nail; Arıkan, Erdal
Asynchronous Transfer Mode (ATM) networks have inputs which consist of superpositions of correlated cell streams. Markov modulated processes are commonly used to characterize this correlation. The first step through gaining an analytical insight in the performance issues of an ATM network is the analysis of a single channel. One objective of this study is the performance analysis of an ATM multiplexer whose input is a Markov modulated periodic arrival process. Based on the transient behavior of the nD/D/1 queue, we present an approximate method to compute the queue length distribution accurately. The method reduces to the solution of a linear differential equation with variable coefficients. Another general traffic model is the Markov Modulated Poisson Process (MMPP). We employ Pade approximations in transform domain for the deterministic service time distribution in an M MPP/D/1 queue so as to compute the distribution of the buffer occupancy. For both models, we also provide algorithms for analysis in the case of finite queue capacities and for computation of effective bandwidth.
Open Access
PLAWE: A piecewise linear circuit simulator using asymptotic waveform evaluation
(Bilkent University, 1994) Topçu, Satılmış; Atalar, Abdullah
A new circuit simulation program, PLAWE, is developed for the transient analysis of VLSI circuits. PLAWE uses Asymptotic Waveform Evaluation (AWE) technique, which is a new method to analyze linear(ized) circuits, and Piecewise Linear (PWL) approach for DC representation of nonlinear elements. AWE employs a form of Pade approximation rather than numerical integration techniques to approximate the response of linear(ized) circuits in either the time or the frequency domain. AWE is typically two or three orders of magnitude faster than traditional simulators in analyzing large linear circuits. However, it can handle only linear(ized) circuits, while the transient analysis problem is generally nonlinear due to the presence of nonlinear devices such as diodes, transistors, etc.. We have applied the AWE technique to the transient simulation of nonlinear circuits by using static PWL models for nonlinear elements. But, finding a good static PWL model which fits well to the actual i — v characteristics of a nonlinear device is not an easy task and in addition, static PWL modelling results in low accuracy. Therefore, we have developed a dynamic PWL modeling technique which uses SPICE models for nonlinear elements to enhance the accuracy of the simulation while preserving the efficiency gain obtained with AWE. Hence, there is no modelling problem and we can adjust the accuracy level by varying some parameters. If the required level of accuracy is increased, more simulation time is needed. Practical examples are given to illustrate the significant improvement in accuracy. For circuits containing especially weakly nonlinear devices, this method is typically at least one order of magnitude faster than HSPICE. A fast and convergent iteration method for piecewise-linear analysis of nonlinear resistive circuits is presented. Most of the existing algorithms are applicable only to a limited class of circuits. In general, they are either not convergent or too slow for large circuits. The new algorithm presented in this thesis is much more efficient than the existing ones and can be applied to any piecewise-linear circuit. It is based on the piecewise-linear version of the Newton-Raphson algorithm. As opposed to the NewtonRaphson method, the new algorithm is globally convergent from an arbitrary starting point. It is simple to understand and it can be easily programmed. Some numerical examples are given in order to demonstrate the effectiveness of the presented algorithm in terms of the amount of computation.
Open Access
Fast algorithms for linear and nonlinear microwave circuit simulation
(Bilkent University, 1994) Çelik, Mustafa; Atalar, Abdullah
A new method is proposed for dominant pole-zero (or pole-residue) analysis of large linear microwave circuits containing both lumped and distributed elements. This method is based on a multipoint Fade approximation. It finds a reduced order rational s-domain transfer function using a data set obtained by solving the circuit at only a few frequency points. We propose two techniques in order to obtain the coefficients of the transfer function from the data set. The proposed method provides a more efficient computation of both transient and frequency domain responses than conv'entional simulators and more accurate results than the techniques based on single-point Fade approximation such as Asymptotic Waveform Evaluation. This study also describes a new method for the transient analysis of large circuits containing weakly nonlinear elements, linear lumped components, and the linear elements specified with frequency domain parameters such as lossy multiconductor transmission lines. The method combines the Volterra-series technique with Asymptotic Waveform Evaluation approach and corresponds to recursive analysis of a linear equivalent circuit. We have also proposed a new method to find steady state responses of nonlinear microwave circuits. It is a modified and more efficient form of Newton-Raphson iteration based harmonic balance (HB) technique. It solves the convergence problems of the HB technique at high drive levels. The proposed method makes use of the parametric dependence of the circuit responses on the excitation level. It first computes the derivatives of the complex amplitudes of the harmonics with respect to the excitation level efficiently and then finds the Fade approximants for the amplitudes of the harmonics using these derivatives.
Open Access
Three-dimensional facial motion and structure estimation in video coding
(Bilkent University, 1994) Bozdağı, Gözde; Onural, Levent
We propose a novel formulation where 3-D global and local motion estimation and the adaptation of a generic wire-frame model to a particular speaker are considered simultaneously within an optical flow based framework including the photometric effects of the motion. We use a flexible wire-frame model whose local structure is characterized by the normal vectors of the patches which are related to the coordinates of the nodes. Geometric constraints that describe the propagation of the movement of the nodes are introduced, which are then efficiently utilized to reduce the number of independent structure parameters. A stochastic relaxation algorithm has been used to determine optimum global motion estimates and the parameters describing the structure of the wire-frame model. For the initialization of the motion and structure parameters, a modified feature based algorithm is used whose performance has also been compared with the existing methods. Results with both simulated and real facial image sequences are provided.
Open Access
New methods for robust speech recognition
(Bilkent University, 1995) Erzin, Engin; Çetin, A. Enis
New methods of feature extraction, end-point detection and speech enhcincement are developed for a robust speech recognition system. The methods of feature extraction and end-point detection are based on wavelet analysis or subband analysis of the speech signal. Two new sets of speech feature parameters, SUBLSF’s and SUBCEP’s, are introduced. Both parameter sets are based on subband analysis. The SUBLSF feature parameters are obtained via linear predictive analysis on subbands. These speech feature parameters can produce better results than the full-band parameters when the noise is colored. The SUBCEP parameters are based on wavelet analysis or equivalently the multirate subband analysis of the speech signal. The SUBCEP parameters also provide robust recognition performance by appropriately deemphasizing the frequency bands corrupted by noise. It is experimentally observed that the subband analysis based feature parameters are more robust than the commonly used full-band analysis based parameters in the presence of car noise. The a-stable random processes can be used to model the impulsive nature of the public network telecommunication noise. Adaptive filtering are developed for Q-stable random processes. Adaptive noise cancelation techniques are used to reduce the mismacth between training and testing conditions of the recognition system over telephone lines. Another important problem in isolated speech recognition is to determine the boundaries of the speech utterances or words. Precise boundary detection of utterances improves the performance of speech recognition systems. A new distance measure based on the subband energy levels is introduced for endpoint detection.
Open Access
Robust sampled-data control
(Bilkent University, 1995) Ocalı, Ogan; Sezer, Erol
Robust control of uncertain plants is a major area of interest in control theory. In this dissertation, robust stabilization of plants under various classes of structural perturbations using sampled-data controllers is considered. It is shown that a controllable system under bounded perturbations that satisfy certain structural conditions can be stabilized using high-gain sampled-data state feedback control, provided that the sampling period is sufficiently small, with generalizations to decentralized control of interconnected systems. This result is then modified so as to enable adapting the gain and the sampling periods of controllers online. Finally another design methodology is given which enables the controllers to operate on the sampled values of output only, instead of full state measurements.
Open Access
Performance of two-level forward error correction for lost cell recovery in ATM networks
(Bilkent University, 1995) Oğuz, Nihat Cem; Ayanoğlu, Ender
The major source of errors in Asynchronous Transfer Mode (ATM.) networks is expected to be buffer overflow during congestion, resulting in cell losses. The large ratio of the end-to-end propagation time for a typical connection to the cell transmission time makes lost cell recovery by means of retransmissionbased error control techniques impractical especially for delay-sensitive highspeed applications. As has been shown by many authors, forward error correction is a promising alternative since it can improve end-to-end reliability without requiring retransmissions. This thesis discusses the use of a two-level forward error correction scheme for virtual channel and virtual path connections in ATM networks. The performance of the scheme, which exploits erasure correcting simple and interleaved block codes simultaneously, is studied via both analyses and simulations. For a single-node virtual channel connection, a novel and accurate discrete-time analytical cell loss model is developed first. Based on this model, the reduction in the cell loss rate achieved by two-level coding is then investigated extensively via iterative computational methods. For the case of a four-node, long-distance virtual channel connection that cannot tolerate any loss, the use of the two-level coding scheme in conjunction with an automatic repeat request mechanism is considered, and detailed simulations are made to quantify the improvement achieved in the delay-throughput performance. The results obtained indicate substantial performance improvements even for very high network loads provided that an appropriate coding technique is chosen according to the traffic characteristics. Typically, bursty traffic requires code interleaving be used for effective loss recovery whereas small-latency simple block codes suffice for random traffic. Two-level coding, which is shown to effectively combine the fast and burst loss recovery capabilities of the individual coding techniques, is attractive for traffic streams of unpredictable or time-varying characteristics.
Open Access
Analysis of cylindrical reflector antennas in the presence of circular radomes by complex source-dual series approach
(Bilkent University, 1996) Oğuzer, Taner; Altıntaş, Ayhan
The radiation from cylindrical reflector antennas is analyzed in an accurate manner for both H and E polarization cases. The problem is first formulated in terms of the dual series equations and then it is regularized by the Riemann Hilbert Problem technique. The resulting matrix equation is solved numerically with a guaranteed accuracy, and remarkably little CPU time is needed. The feed directivity is included in the analysis by the complex source point method. Various characteristic patterns are obtained for the front and offset-fed reflector antenna geometries with this analysis and some comparisons are made with the high frequency techniques. The directivity and radiated power properties are also studied. Furthermore, the results are also compared by the .Method Of Moments and Physical Optics solutions. Then the case of circular radome enclosing the reflector is considered. Radomes concentric with the reflector are examined first, followed by the non-concentric radomes.
Open Access
Repeated filtering in consecutive fractional Fourier domains
(Bilkent University, 1997) Erden, M. Fatih; Özaktaş, Haldun M.
In the first part of this thesis, relationships between the fractional Fourier transformation and Fourier optical systems are analyzed to further elucidate the importance of this transformation in optics. Then in the second part, the concept of repeated filtering is considered. In this part, the repeated filtering method is interpreted in two different ways. In the first interpretation the linear transformation between input and output is constrained to be of the form of repeated filtering in consecutive domains. The applications of this constrained linear transformation to signal synthesis (beam shaping) and signal restoration are discussed. In the second interpretation, general linear systems are synthesized with repeated filtering in consecutive domains, and the synthesis of some important linear systems in signal processing and the .synthesis of optical interconnection architectures are considered for illustrative purposes. In all of the examples, when our repeated filtering method is compared with single domain filtering methods, significant improvements in performance are obtained with only modest increases in optical or digital implementation costs. Similarly, when the proposed method is compared with general linear systems, it is seen that acceptable performance may be possible with significant computational savings in implementation costs.
Open Access
A framework for handling connectionless services in ATM networks
(Bilkent University, 1997) Abdelati, Mohamed; Arıkan, Erdal
ATM networks, which are connection-oriented transport inediums, are well-suited to handle interactive and real-time applications such as telephony and video conferencing. However, they will be underutilized if used directly in aipplications characterized by sporadic behaivior and short service time requirements such as mail and file transfer. For such applications, in which the user information typically consists of a single block of data., connection-oriented services are inefficient due to connection establishment and teardown overhead. These applications are more efficiently handled by a connectioidess service which multiplexes data from individual applications into a pre-established virtual connection. In this work a method for providing connectionless services in ATM networks is proposed. This method is based on a pricing scheme which allocates the communication resources in a Pareto-optimal way that achieves maximum total surplus. The key idea, is to decompose the service provision procedure among three separate parties whose interactions are governed by a. set of competitive pricing mechanisms.
Open Access
Object-based 3-d motion and structure analysis for video coding applications
(Bilkent University, 1997) Alatan, A. Aydin; Onural, Levent
Novel 3-D motion analysis tools, which can be used in object-based video codecs, are proposed. In these tools, the movements of the objects, which are observed through 2-D video frames, are modeled in 3-D space. Segmentation of 2-D frames into objects and 2-D dense motion vectors for each object are necessary as inputs for the proposed 3-D analysis. 2-D motion-based object segmentation is obtained by Gibbs formulation; the initialization is achieved by using a fast graph-theory based region segmentation algorithm which is further improved to utilize the motion information. Moreover, the same Gibbs formulation gives the needed dense 2-D motion vector field. The formulations for the 3-D motion models are given for both rigid and non- rigid moving objects. Deformable motion is modeled by a Markov random field which permits elastic relations between neighbors, whereas, rigid 3-D motion parameters are estimated using the E-matrix method. Some improvements on the E-matrix method are proposed to make this algorithm more robust to gross errors like the consequence of incorrect segmentation of 2-D correspondences between frames. Two algorithms are proposed to obtain dense depth estimates, which are robust to input errors and suitable for encoding, respectively. While the former of these two algorithms gives simply a MAP estimate, the latter uses rate-distortion theory. Finally, 3-D motion models are further utilized for occlusion detection and motion compensated temporal interpolation, and it is observed that for both applications 3-D motion models have superiority over their 2-D counterparts. Simulation results on artificial and real data show the advantages of the 3-D motion models in object-based video coding algorithms.
Open Access
A novel CAD algorithm for the analysis of printed geometries
(Bilkent University, 1997) Kınayman, Noyan; Aksun, M. I.
An efficient and accurate computer aided design (CAD) software for the electromagnetic simulation of passive microwave components, fabricated in planar stratified media, is developed in this work. The numerical technique employed in this software is based on the spatial-domain method of moments (MoM) in conjunction with the closed-form Green’s functions. Since the computational efficiency is a major issue in CAD softwares, the spatial-domain MoM is significantly improved in this respect with the use of the closed-form Green’s functions and closed-form expressions for the MoM matrix entries. Vertical metalizations in the form of via holes and shorting pins, which are the indispensable parts of the most microwave circuits, are also modeled very efficiently and incorporated into this formulation. The resulting approach is applied to some realistic microwave circuits and planar antennas, with and without vertical metalizations, to validate the formulation. It is also demonstrated that the formulation developed in this work can be efficiently used with an optimization algorithm for design purposes. The results obtained from the formulation proposed in this work are compared to those obtained from a commercial electromagnetic analysis software.
Open Access
Image coding for digitized libraries
(Bilkent University, 1998) Gerek, Ömer Nezih; Çetin, A. Enis
III this thesis, image coding methods for two basic image types are developed under a digitized library framework. The two image types are gray tone or color images, and binary textual images, which are the digitized image versions of text documents. The grciy tone images are encoded using an adaptive subband decomposition followed by zerotree quantizers. The adaptive sub- l)and decomposition filter bank adaptively updates the filter bank coefficients in which the values of one of the subbands is predicted from the other sub- band. It is observed that the adaptive subband decomposition performs better than a regulcir subband decomposition with a fixed filter bank in terms of compression. For the binary textual images, a compression algorithm using binary subband decomposition followed by a textual image compression (TIC) method that exploits the redundancy in repeating characters is developed. The binary subband decomposition yields binary sub-images, and the TIC method is applied to the low band sub-image. Obtaining binary sub-images improves compression results as well as pattern matching time of the TIC method. Simulation results for both adaptive subband decomposition and multiresolution TIC methods indicate improvements over the methods described in the literature.
Open Access
Noise analysis of interdigital cantilevers for atomic force microscopy
(Bilkent University, 1998) Yaralıoğlu, G. Göksenin; Atalar, Abdullah
Atomic force microscoiDe (AFM) is proved to be a powerful tool for atomic resolution surface imaging. The most crucial parts of an AFM system are the cantilever with an integrated tip and the deflection detection sensor. AFM systems measure deflections that are comparable to atomic dimensions using technicpies such as tunneling, interferometry, piezoresistive sensing and optical lever detection. Interdigital (ID) cantilevers are the most recently introduced method which makes use of its interferometric nature to improve deflection detection sensitivity. Basicallj^ ID cantilever is composed of two sets of interleaving fingers which create an optical phase grating. In this thesis, a detailed analysis of ID cantilevers will be presented. The theory underlying the o[)eration of the phase gratings with the response curves curd confirming e.xperimental results will be formulated. The noise performance of the ID cantilever will be compared to the optical lever detection method. We will present a new method for the mechaniccd noise calculation by using the analogy between electrical circuits and mechanical structures. This new method will be applied to the AFM cantilevers to calculate the noise correlation on the cantilever surface. We will also present the signal to noise ratio (SNR) calculation method on the cantilever. One of the basic problem of the all AF'M systems is the speed limitation due to single AF'M tip scanning at relatively low frequencies yielding low throughput. A direct approach to this problem is the operation of cantilever arrays instead of one cantilever. In this thesis, we will also present the electronics for cantilever arrays which increases the throughput of the AFM systems.
Open Access
Circuit theoretical methods for efficient solution of finite element structural mechanics problems
(Bilkent University, 1999) Ekinci, Ahmet Suat; Atalar, Abdullah
Shrinking device dimensions in integrated circuit technology made integrated circuits with millions of components a reality. As a result of this advance, electrical circuit simulators that can handle very large number of components have emerged. These programs use new circuit simulation techniques which approximate the system with reduced order models, and can find solutions accurately and quickly. This study proposes formulating the structural mechanics problems using FEM, and then employing the recent speedup techniques used in circuit simulation. This is obtained by generating an equivalent resistor-inductor-capacitor circuit containing controlled sources. We analyze the circuits with general-purpose circuit simulation programs, HSPICE, and an in-house developed circuit simulation program, MAWE, which makes use of generalized asymptotic waveform evaluation (AWE) technique. AWE is a moment matching technique that has been successfully used in circuit simulation for solutions of large sets of equations. Several examples on the analysis of the displacement distributions in rigid bodies have shown that using circuit simulators instead of conventional FEM solution methods improves simulation speed without a significant loss of accuracy. Pole analysis via congruence transformations (PACT) technique is a recent algorithm used for obtaining lower order models for large circuits. For a further reduction in time, we employed a similar algorithm in structural mechanics problems before obtaining the equivalent circuit. The results are very promising.
Open Access
Computer aided diagnosis in radiology
(Bilkent University, 1999) Gürcan, Metin Nafi; Çetin, A. Enis
Breast cancer is one of the most deadly diseases for middle-aged women. In this thesis, computer-aided diagnosis tools are developed for the detection of breast cancer on mammograms. These tools include a detection scheme for microcalcification clusters which are an early sign of breast cancer, and a method to detect the boundaries of mass lesions. In the first microcalcification detection method we propose, a subband decomposition structure is employed. Contrary to the previous work, the detection is carried out in the subband domain. The mammogram image is first processed by a subband decomposition filter bank. The resulting subimage is analyzed to detect microcalcification clusters. In regions corresponding to the healthy breast tissue the distribution is almost Gaussian. Since microcalcifications are small, isolated bright spots, they produce outliers in the subimages and the distribution of pixels deviates from Gaussian. The subimages are divided into overlapping square regions. In each square region, skewness and kurtosis values are estimated. As third and fourth order correlation parameters, skewness and kurtosis, are measures of the asymmetry and impulsiveness of the distribution, they can be used to find the locations of microcalcification clusters. If the values of these parameters are higher than experimentally determined thresholds then the region is marked as a potential cancer area. Experimental studies indicate that this method successfully detects regions containing microcalcifications. We also propose another microcalcification detection method which uses two- dimensional (2-D) adaptive filtering and a higher order statistics based Gaussianity test. In this method, statistics of the prediction errors are computed to determine whether the samples are from a Gaussian distribution. The prediction error sequence deviates from Gaussianity around microcalcification locations because prediction of microcalcification pixels is more difficult than prediction of the pixels corresponding to healthy breast tissue. Then, we develop a new Gaussianity test which has higher sensitivity to outliers. The scheme which uses this test gives better detection performance compared to the previously proposed methods. Within the detected regions it is possible to segment individual microcalcifications. An outlier labeling and nonlinear subband decomposition based microcalcification segmentation method is also investigated. Two types of lesions, namely mass and stellate lesions, might be indicators of breast cancer. Finally, we propose a snake algorithm based scheme to detect the boundaries of mass lesions on mammograms. This scheme is compared with a recently developed region growing based boundary detection method. It is observed that the snake algorithm results in a more smooth boundary which is consistent with the morphological structure of mass lesions.