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By generating Fourier descriptors based upon the waveform induced by a pattern's geometric projection, a number of classic difficulties with the Fourier-descriptor methodology are mitigated. Not only are the descriptors invariant with respect to scale, translation, and rotation (as is usually the case), they are also continuous in the Hausdorff metric and robust with respect to both point noise and occlusion. An additional advantage is that they can be computed relative to a thresholded image without first finding an edge, thereby avoiding the difficulties typically present in thinning and orientation determination. The present paper discusses the method of projection-generated Fourier descriptors, as well as a study of the sensitivity to point noise. A companion paper will present the morphological properties and the effect of pattern occlusion.

Analysis of the noise voltage density evaluation procedures of the ultrasonic preamplifier is presented. Ultrasonic testing is demanding low noise reception channel. Techniques and equipment for ultrasonic preamplifier's noise performance evaluation are suggested. Equipment used and measurement technologies applied are described. One of the techniques suggested allows estimating the preamplifier noise with only impedance measurement results available. Sine wave correlation technique was used in the impedance measurement procedure. Another technique, not demanding the spectrum analyzer, was suggested, which uses the analog-to-digital converter (ADC) sampling and the Fourier transform to obtain the noise spectral density. Experimental results for the measured complex gain and the equivalent input noise of the preamplifier are presented. Comparison with traditional noise estimation procedure, using the spectrum analyzer is given. Both direct measurement techniques (ADC record Fourier analysis based and spectrum analyzer) indicated good match. Noise whiteness was estimated: in a region of operation frequencies, 5–7 MHz, noise can be considered as white.

The cyclic A/D converting process is equivalent to iterations of a chaotic may using symbolic dynamics. The principle can be extended to construct "general cyclic ADCs" based on chaotic iterations. In this paper, the two necessary conditions of iterated maps are presented, and the new attributes of these converters are also discussed. By establishing a noise model, the analytic expressions of the random and system errors in general cyclic ADCs are derived and verified by simulations. With the same level of additive white noise, the optimal iterative maps for general cyclic ADCs are deduced.

The parabolic equation approximation method is applied to build the model of the vertical spatial correlation and vertical directivity characteristics of ocean ambient noise under varying environment. The random noise sources which have the same intensity are represented by uncorrelated monopoles distributed uniformly over an infinite plane located a certain depth below the sea surface. The spatial properties of noise field are analyzed under the varying ocean environments which are the slope, seamount and varying sound speed profiles. According to the results of simulation, the varying environment changes the propagating paths of noise, so the spatial properties (correlation and directionality) of the noise field change. When the remote noise intensity increases, the noise intensity in low grazing angle and the vertical correlations of nose field become stronger. At last, the experiment’s results support the results of simulation.

Algorithms for the estimation of noise level and the detection of noise model are proposed. They are applied to gene expression data for Drosophila embryos. The 2D data on gene expression and the extracted 1D profiles are considered. Since the 1D data contain processing errors, an algorithm for separation of these processing errors is constructed to estimate the biological noise level. An approach to discrimination between the additive and multiplicative models is suggested for the 1D and 2D cases. Singular spectrum analysis and its 2D extension are exploited for the pattern extraction. The algorithms are tested on artificial data similar to the real data. Comparison of the results, which are obtained by the 1D and 2D methods, is performed for Krüppel and giant genes.

Scanning electron microscopy (SEM) is of great significance for analyzing the ultrastructure. However, due to the requirements of data throughput and electron dose of biological samples in the imaging process, the SEM image of biological samples is often occupied by noise which severely affects the observation of ultrastructure. Therefore, it is necessary to analyze and establish a noise model of SEM and propose an effective denoising algorithm that can preserve the ultrastructure. We first investigated the noise source of SEM images and introduced a signal-related SEM noise model. Then, we validated the effectiveness of the noise model through experiments, which are designed with standard samples to reflect the relation between real signal intensity and noise. Based on the SEM noise model and traditional variance stabilization denoising strategy, we proposed a novel, two-stage denoising method. In the first stage variance stabilization, our VS-Net realizes the separation of signal-dependent noise and signal in the SEM image. In the second stage denoising, our D-Net employs the structure of U-Net and combines the attention mechanism to achieve efficient noise removal. Compared with other existing denoising methods for SEM images, our proposed method is more competitive in objective evaluation and visual effects. Source code is available on GitHub (https://github.com/VictorCSheng/VSID-Net).

We present a soft computing approach to character recognition from printed documents. For feature extraction, we define a number of fuzzy sets on the Hough transform of character pattern pixels and synthesize additional fuzzy sets by t-norms. The height of each t-norm constitutes a feature element and a set of 'n' such feature elements form an n-dimensional feature vector for the character. A 3n-dimensional vector is then generated from the n-dimensional feature vector by defining three linguistic fuzzy sets, namely, weak, moderate and strong. These 3n-dimensional vectors form a Multilayer Perceptron (MLP) input for training by back propagation. The MLP outputs represent fuzzy sets denoting the belongingness of an input pattern to a number of fuzzy pattern classes. The feature set is chosen by optimizing a Feature Quality Index (FQI) using genetic algorithm. A two-state Markov chain is used to model degraded document images for simulation tests. The system can recognize characters with an accuracy of 98%.