Detecting left ventricular endocardial and epicardial boundaries by digital two-dimensional echocardiography

Cardiac function is evaluated using echocardiographic analysis of shape attributes, such as the heart wall thickness or the shape change of the heart wall boundaries. This requires that the complete boundaries of the heart wall be detected from a sequence of two-dimensional ultrasonic images of the heart. The image segmentation process is made difficult since these images are plagued by poor intensity contrast and dropouts caused by the intrinsic limitations of the image formation process. Current studies often require having trained operators manually trace the heart walls. A review of previous work is presented, along with how this problem can be viewed in the context of the computer vision area. A novel algorithm is presented for detecting the boundaries. This algorithm first detects spatially significant features based on the measurement of image intensity variations. Since the detection step suffers from false alarms and missing boundary points, further processing uses high-level knowledge about the heart wall to label the detected features for noise rejection and to fill in the missing points by interpolation.     

Design of two-dimensional IIR digital filters by using a novel hybrid optimization algorithm

This paper proposes a hybrid optimization algorithm named as BBO–PSO, which is a combination of biogeography-based optimization (BBO) and particle swarm optimization (PSO). In BBO–PSO, the whole population will be split into several subgroups and BBO is employed for local search in each subgroup independently to achieve the different local optima while PSO is employed for global search based on the local optima to achieve the global optimum. The test results on the benchmark functions show that BBO–PSO has powerful search ability with great robustness. Furthermore, the proposed algorithm is applied to the design of the 2-D IIR digital filters and the simulation results show that it outperforms the existing methods on this problem.     

Stability test for two-dimensional recursive digital filters using inner determinants

A recently introduced stability criterion for two-dimensional digital filters is implemented by decision algebra. The proposed test takes the form of a local positivity test applied to a two-variable polynomial with real coefficients. Two non-trivial examples are given to illustrate the procedure.     

Design of two-dimensional digital filters using singular-valuedecomposition and balanced approximation method

It is shown that the singular-value decomposition (SVD) of the sampled amplitude response of a two-dimensional (2-D) digital filter possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD can be applied along with 1-D finite impulse response (FIR) techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ωΨω₂) plane. The balanced approximation method is applied to linear-phase 2-D FIR filters of the type that may be obtained by using the SVD method. The method leads to economical and computationally efficient filters, usually infinite impulse response filters, which have prescribed amplitude responses and whose phase responses are approximately linear     

Segmenting articular cartilage automatically using a voxel classification approach

We present a fully automatic method for articular cartilage segmentation from magnetic resonance imaging (MRI) which we use as the foundation of a quantitative cartilage assessment. We evaluate our method by comparisons to manual segmentations by a radiologist and by examining the interscan reproducibility of the volume and area estimates. Training and evaluation of the method is performed on a data set consisting of 139 scans of knees with a status ranging from healthy to severely osteoarthritic. This is, to our knowledge, the only fully automatic cartilage segmentation method that has good agreement with manual segmentations, an interscan reproducibility as good as that of a human expert, and enables the separation between healthy and osteoarthritic populations. While high-field scanners offer high-quality imaging from which the articular cartilage have been evaluated extensively using manual and automated image analysis techniques, low-field scanners on the other hand produce lower quality images but to a fraction of the cost of their high-field counterpart. For low-field MRI, there is no well-established accuracy validation for quantitative cartilage estimates, but we show that differences between healthy and osteoarthritic populations are statistically significant using our cartilage volume and surface area estimates, which suggests that low-field MRI analysis can become a useful, affordable tool in clinical studies.     

VLSI implementation of two-dimensional digital filters via two-dimensional filter chips

The realization of an arbitrary two-dimensional (2-D) rational transfer function which represents an infinite impulse response (IIR) 2-D filter in terms of low-order 2-D polynomials is discussed. These low-order polynomials are implemented via a bit-sliced chip, and are used as standard building blocks for the implementation of the general 2-D digital filter. Different general realization methods are considered and are modified in order to incorporate the standard 2-D chips. The resulting structures have reduced complexity and they exhibit a high degree of regularity and modularity. Furthermore, the number of 2-D low-order filter chips required for the implementation of the given filter is substantially reduced, compared to the number of 1-D chips required by regular general implementations.     

Accuracy of q-space related parameters in MRI: simulations and phantom measurements

The accuracy of q-space measurements was evaluated at a 3.0-T clinical magnetic resonance imaging (MRI) scanner, as compared with a 4.7-T nuclear magnetic resonance (NMR) spectrometer. Measurements were performed using a stimulated-echo pulse-sequence on n-decane as well as on polyethylene glycol (PEG) mixed with different concentrations of water, in order to obtain bi-exponential signal decay curves. The diffusion coefficients as well as the modelled diffusional kurtosis K(fit) were obtained from the signal decay curve, while the full-width at half-maximum (FWHM) and the diffusional kurtosis K were obtained from the displacement distribution. Simulations of restricted diffusion, under conditions similar to those obtainable with a clinical MRI scanner, were carried out assuming various degrees of violation of the short gradient pulse (SGP) condition and of the long diffusion time limit. The results indicated that an MRI system can not be used for quantification of structural sizes less than about 10 microm by means of FWHM since the parameter underestimates the confinements due to violation of the SGP condition. However, FWHM can still be used as an important contrast parameter. The obtained kurtosis values were lower than expected from theory and the results showed that care must be taken when interpreting a kurtosis estimate deviating from zero.     

Determination of quantization error in two-dimensional digital filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the following computation J = Σm=0^∞Σn=0^∞y²(m, n). In this paper general method for the evaluation of J based on Laurent expansion of the integrand is presented. Illustrative example for such a computation is given. Notations: We denote with V^-2= {(z1, z2): |z1| ≤ 1, |z2| ≤ 1} the closed unit bidisc, with V²= {(z1, z2): |z1| < 1, |z2| < 1} the open unit bidisc, and with T2= {(z1, z2): |z1| = 1, |z2| = 1} the distinguished boundary of the unit bidisc.     

Stabilization of certain two-dimensional recursive digital filters

A possible extension of a well-known stabilization technique for one-dimensional recursive digital filters to the two-dimensional case was proposed by Shanks via a conjecture, stating that the planar least squares inverse of a two-dimensional filter polynomial is minimum phase and hence stable. In the present work, the conjecture has been verified first for a class of polynomials which are linear in one variable and quadratic in the other and then extended to a class of polynomials of higher degrees in the same variables. Though the conjecture is known to be false, in general, some conditions under which the conjecture is valid are explored.     

Asymptotic stability of two-dimensional digital filters underquantization

The stability of 2-D digital filters implemented with two's complement quantization is investigated. The difference equation model is considered for the following cases: (i) quantization after each product and (ii) quantization after a complete sum of products. For both cases, sufficient conditions are established for asymptotic stability. The 2-D state-space Roesser's (1975) model is also considered under two's complement quantization, and a sufficient condition is derived for its stability. Some examples are given to illustrate the results     

A shape-space-based approach to tracking myocardial borders and quantifying regional left-ventricular function applied in echocardiography

This paper presents a new semi-automatic method for quantifying regional heart function from two-dimensional echocardiography. In the approach, we first track the endocardial and epicardial boundaries using a new variant of the dynamic snake approach. The tracked borders are then decomposed into clinically meaningful regional parameters, using a novel interpretational shape-space motivated by the 16-segment model used in clinical practice for qualitative assessment of heart function. We show how a quantitative and automatic scoring scheme for the endocardial excursion and myocardial thickening can be derived from this. Results illustrating our approach on apical long-axis two-chamber-view data from a patient with a myocardial infarct in the apical anterior/inferior region of the heart are presented. In a case study (five patients, nine data sets) the performance of the tracking and interpretation techniques are compared with manual delineations of borders using a number of quantitative measures of regional comparison.     

On the approximation of the magnitude response of two-dimensional IIR digital filters using linear programming

The design of two-dimensional IIR digital filters is approached using linear-programming techniques. The problem is formulated as an approximation problem and filter frequency response characteristics are represented via the square of the magnitude of the filter transfer function. An appropriate approximation error is minimized leading to a linear problem formulation. The latter problem does not require differential correction methods for its solution, thus resulting in a computationally efficient algorithm. Stability conditions and symmetry considerations are easily accounted for. The linear programming approach assures convergence of the solution to a global minimum, among other advantages over nonlinear methods. Several examples illustrate the strength and effectiveness of the methodology.     

A simple deductive proof of a stability test for two-dimensional digital filters

A simple proof based on a continuity argument is proposed for a theorem on the stability tests of two-dimensional (2-D) digital filters, independently proposed by Strintzis and by DeCarlo, Murray, and Saeks.     

Design of two-dimensional digital filters via spectral transformations

Complex maps, with domains and codomains consisting of rational transfer functions, have often been used in designing two-dimensional (2-D) digital filters. Such maps, commonly known as spectral transformations, have the important property of carrying a stable rational transfer function to another stable rational function. This paper presents a unified framework for designing 2-D stable digital filters from prescribed magnitude-response specifications using spectral transformations such that the magnitude response of the resultant approximation is sort of a "best" approximation of the given specification. It is shown that there are two basic strategies for such designs, each with its own advantages and disadvantages. The design procedures are illustrated with practical examples. Further, it is also shown that all earlier results on 2-D filter design using spectral transformations follow as special cases of the general theory presented here.     

Analogue multiplexing using a digital technique

A digital technique of multiplexing analogue signals is described whereby improved isolation between channels and negligible equivalent-channel `on? resistance is achieved. It is also suggested that the proposed method may find application in analogue?digital conversion     

Necessary conditions for stability and a simple stabilisationscheme for two-dimensional digital filters

The letter describes a set of necessary stability conditions which form the basis of a new fast testing procedure, followed by a simple stabilisation scheme. An example is given