Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part fo the edge detection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus we consider this part of edge detection as a problem in numerical differentiation. We show that numerical differentiation of images is an ill-posed problem in the sense of Hadamard. Differentiation needs to be regularized by a regularizing filtering operation before differentiation. This shows that his part of edge detection consists of two steps, a filtering step and differentiation step.

We will briefly outline a computational theory of the first stages of human vision according to which (a) the retinal image is filtered by a set of centre-surround receptive fields (of about 5 different spatial sizes) which are approximately bandpass in spatial frequency and (b) zero-crossings are detected independently in the output of each of these channels. Zero-crossings in each channel are then a set of discrete symbols which may be used for later processing such as contour extraction and stereopsis. A formulation of Logan's zero-crossing results is proved for the case of Fourier polynomials and an extension of Logan's theorem to 2-dimentsional functions is also approved. Within this framework, we shall describe an experimental and theoretical approach (developed by one of us with M. Fahle) to the problem of visual acuity and hyperacuity of human vision. The positional accuracy achieved, for instance, in reading a vernier is astonishingly high, corresponding to a fraction of the spacing between adjacent photoreceptors in the fovea. Stroboscopic presentation of a moving object can be interpolated by our visual system into the perception of continuous motion; and this "spatio-temporal" interpolation also can be very accurate. It is suggested that the known spatiotemporal properties of the channels envisaged by the theory of visual processing outlined above implement an interpolation scheme which can explain human vernier acuity for moving targets.

Computational theories of structure-from-motion and stereo vision only specify the computation of three-dimensional surface information at points in the image at which the irradiance changes. Yet, the visual perception is clearly of complete surfaces, and this perception is consistent for different observers. Since mathematically the class of surfaces which could pass through the known boundary points provided by the stereo system is infinite and contains widely varying surfaces, the visual system must incorporate some additional constraints besides the known points in order to compute the complete surface. Using the image irradiance equation, we derive the surface consistency constraint, informally referred to as no news is good news. The constraint implies that the surface must agree with the information from stereo or motion correspondence, and not vary radically between these points. An explicit form of this surface consistency constraint is derived, by relating the probability of a zero-crossing in a region of the image to the variation in the local surface orientation of the surface, provided that the surface albedo and the illumination are roughly constant. The surface consistency constraint can be used to derive an algorithm for reconstructing the surface that "best" fits the surface information provided by stereo or motion correspondence.

This master's thesis describes basics principles of QRS complex detection. It is focused on QRS detection using zero crossing counts method. There are described princips and program realization of this method. The other part is focused on genetic optimalization algorithm. There are presented obtained optimalization results on standard CSE and MIT-BIH database. The quality of the detector is compared with other authors. The optimalized QRS detector achieves comparable results with other authors. The part of the thesis is graphical user interface which supply view on modified ECG signal and detection results.

Cette thèse porte sur le recalage de signaux à partir de l'alignement de leurs landmarks, pour la comparaison d'ensembles de courbes ou d'images. Après une revue des techniques de recalage qui existent dans la littérature, une approche nonparamétrique est proposée pour estimer les landmarks d'une fonction 1D bruitée à partir des lignes de maxima d'ondelettes et de zero-crossings de sa transformée continue en ondelettes. Un nouvel outil, l'intensité structurelle, est introduit pour représenter les positions des points caractéristiques d'une courbe sous forme d'une densité de probabilité. Cette méthode conduit à une nouvelle technique de mise en correspondance automatique des landmarks de deux fonctions. L'approche envisagée dans le cas 1D est étendue au cas 2D en utilisant des décompositions en wedgelets/platelets pour détecter les contours d'une image. De nombreuses simulations et des problèmes réels d'analyse de variance fonctionnelle servent d'illustration des méthodes proposées.

We consider real zero-crossing analysis of the real/imaginary parts of the spectrum, namely, spectral zero-crossings (SZCs). The two major contributions are to show that: (i) SZCs provide enable temporal localization of transients; and (b) SZCs are suitable for modeling transient signals. We develop a spectral dual of Kedem’s result linking temporal zero-crossing rate (ZCR) to the spectral centroid. The key requirement is stationarity, which we achieve through random-phase modulations of the time-domain signal. Transient signals are not amenable to modelling in the time domain since they are bursts of energy localized in time and lack structure. We show that the spectrum of transient signals have a rich modulation structure, which leads to an amplitude-modulation – frequency-modulation (AM-FM) model of the spectrum. We generalize Kedem’s arc-cosine formula for lags greater than one. For the specific case of a sinusoid in white Gaussian noise, He and Kedem devised an iterative filtering algorithm, which leads to a contraction mapping. An autoregressive filter of order one is employed and the location of the pole is the parameter that is updated based on the filtered output. We use the higher-order property, which relates the autocorrelation to the expected ZCR of the filtered process, between lagged ZCR and higher-lag autocorrelation to develop an iterative higher-order autoregressive-filtering scheme, which stabilizes the ZCR and consequently provides robust estimates of the autocorrelation at higher lags. Next, we investigate ZC properties of critically sampled outputs of a maximally decimated M-channel power complementary analysis filterbank (PCAF) and derive the relationship between the ZCR of the input Gaussian process at lags that are integer multiples of M in terms of the subband ZCRs. Based on this result, we propose a robust autocorrelation estimator for a signal consisting of a sum of sinusoids of fixed amplitudes and uniformly distributed random phases. Robust subband ZCRs are obtained through iterative filtering and the subband variances are estimated using the method-of-moments estimator. We compare the performance of the proposed estimator with the sample auto-correlation estimate in terms of bias, variance, and mean-squared error, and show through simulations that the performance of the proposed estimator is better than the sample auto- correlation for medium to low SNR. We then consider the ZC statistics of the real/imaginary parts of the discrete Fourier spectrum. We introduce the notion of the spectral zero-crossing rate (SZCR) and show that, for transients, it gives information regarding the location of the transient. We also demonstrate the utility of SZCR to estimate interaural time delay between the left and right head-related impulse responses. The accuracy of interaural time delay plays a vital role in binaural synthesis and a comparison of the performance of the SZCR estimates with that of the cross-correlation estimates illustrate that spectral zeros alone contain enough information for accurately estimating interaural time delay. We provide a mathematical formalism for establishing the dual of the link between zero-crossing rate and spectral centroid. Specifically, we show that the expected SZCR of a stationary spectrum is a temporal centroid. For a deterministic sequence, we obtain the stationary spectrum by modulating the sequence with a random phase unit amplitude sequence and then computing the spectrum. The notion of a stationary spectrum is necessary for deriving counterparts of the results available in temporal zero-crossings literature. The robustness of location information embedded in SZCR is analyzed in presence of a second transient within the observation window, and also in the presence of additive white Gaussian noise. A spectral-domain iterative filtering scheme based on autoregressive filters is presented and improvement in the robustness of the location estimates is demonstrated. As an application, we consider epoch estimation in voiced speech signals and show that the location information is accurately estimated using spectral zeros than other techniques. The relationship between temporal centroid and SZCR also finds applications in frequency-domain linear prediction (FDLP), which is used in audio compression. The prediction coefficients are estimated by solving the Yule-Walker equations constructed from the spectral autocorrelation. We use the relationship between the spectral autocorrelation and temporal centroid to obtain the spectral autocorrelation directly by time-domain windowing without explicitly computing the spectrum. The proposed method leads to identical results as the standard FDLP method but with reduced computational load. We then develop a SZCs-based spectral-envelope and group-delay (SEGD) model, which finds applications in modelling of non-stationary signals such as Castanets. Taking into account the modulation structure and spectral continuity, local polynomial regression is performed to estimate the GD from the real spectral zeros. The SE is estimated based on the phase function computed from the estimated GD. Since the GD estimate is parametric, the degree of smoothness can be controlled directly. Simulation results based on synthetic transient signals are presented to analyze the noise-robustness of the SE-GD model. Applications to castanet modeling, transient compression, and estimation of the glottal closure instants in speech are shown.

This work deals with ECG signal measuring and methods of its processing. It compares some of the QRS detection methods and describes some of the testing databases. In this work a detector of QRS complex is realized, it is based on the approach of zero crossings. Next section makes combination of results from separate leads to one, which improves efficiency of detection. One section of this work deals with design and realization delination of ECG signal. In the last part outputs of this delineation are compared with the results of the other authors.