Sigma Filter Research Articles

Phase‐constrained data extrapolation method for reduction of truncation artifacts

The authors present an improvement to a sigma-filter extrapolation method for the reconstruction of magnetic resonance (MR) images from symmetric discrete Fourier data. By making use of the phase information in the image data, the proposed method can overcome the data inconsistency problem of the original method for handling MR image data with large phase variations, such as those obtained in gradient-echo pulse sequences. Reconstruction results show that its performance is comparable with that of the modified complex sigma-filter method proposed previously to handle the inconsistency problem. However, the new approach has the advantage of reducing computation time by a factor of two with use of a sigma filter applied to real instead of complex images. It is expected that this method will be more practical for use in clinical MR imaging systems.

Pattern and motion vision without Laplacian zero crossings.

The zero crossings of band-limited signals are known to be rich in information. Recent models of information processing in biological visual systems have proposed that image structure is represented initially by such zero crossings, after the image has been bandpass filtered at multiple scales by neural receptive fields whose two-dimensional profiles resemble the Laplacian of a Gaussian. Because the resulting zero crossings generally correspond to physically meaningful structures such as edges and occlusion boundaries, and indeed under some conditions can exhaustively specify the original image, such representations have proven useful and efficient in a variety of machine vision problems. However, some simple information-processing operations that are apparent in human pattern and motion vision can be shown to be impossible in such representations, because the zero crossings in the bandpassed signals do not capture the necessary information (at any scale of analysis), because the information that they provide is misleading, or because there are no such crossings in the signals after delta 2 G sigma filtering at any scale. Examples are provided of simple visual signal-processing tasks (texture discrimination, motion perception, pattern detection) that human beings can perform effortlessly but that cannot be performed in the proposed multiscale delta 2 G sigma zero-crossings schemes. These perceptual capabilities offer evidence against this model of early image representation in human vision.

Adaptive image restoration of sigma filter using local statistics and human visual characteristics

The sigma filter is a nonlinear scheme for modifying an average (mean) filter to improve its edge-preserving characteristic. However, this filter is susceptible to impulsive noise, such as BSC (binary symmetric channel) noise. In this letter, a simple adaptive algorithm for a sigma filter is presented using local image statistics and human visual characteristics to compensate for its drawbacks. Experimental results for an image degraded by BSC noise show that the proposed algorithm has much better performance than nonadaptive ones both on SNR gain and on subjective image quality.

Adaptive filters for digital image noise smoothing: An evaluation

Six adaptive noise filtering algorithms were implemented and evaluated. There are (1) median filtering, (2) K-nearest neighbor averaging, (3) gradient inverse weighted smoothing, (4) sigma filtering, (5) Lee additive and multiplicative filtering, and (6) modified Wallis filtering. For the sake of comparison, the mean filter was also included. All algorithms were tested on noise corrupted copies of a composite image consisting of a uniform field, a bar pattern of periods increasing from 2 to 20 pixels, printed text, and a military tank sitting on desert terrain. In one test, uniformly distributed noise between gray levels of −32 and 32 was added to the composite image and filtered. In a second test, multiplicative Gaussian noise with mean 1.0 and standard deviation 0.25 was introduced, then filtered. A 7×7 pixel processing window was used in all six adaptive algorithms and the mean filter for both tests. An adaptive filter was used iteratively with varying window sizes to demonstrate the success of iterative adaptive smoothing. Filtering results were evaluated from statistics, examination of transects plotted from each filtered bar pattern, and from visual ranking by a group of observers.

Digital image smoothing and the sigma filter

A conceptually simple but effective noise smoothing algorithm is described. This filter is motivated by the sigma probability of the Gaussian distribution, and it smooths the image noise by averaging only those neighborhood pixels which have the intensities within a fixed sigma range of the center pixel. Consequently, image edges are preserved, and subtle details and thin lines such as roads are retained. The characteristics of this smoothing algorithm are analyzed and compared with several other known filtering algorithms by their ability to retain subtle details, preserving edge shapes, sharpening ramp edges, etc. The comparison also indicates that the sigma filter is the most computationally efficient filter among those evaluated. The filter can be easily extended into several forms which can be used in contrast enhancement, image segmentation, and smoothing signal-dependent noisy images. Several test images 128 × 128 and 256 × 256 pixels in size are used to substantiate its characteristics. The algorithm can be easily extended to 3-D image smoothing.

A simple speckle smoothing algorithm for synthetic aperture radar images

Speckles appearing in synthetic aperture radar (SAR) images are generated by the coherent processing of radar signals. Basically the speckles have the nature of a multiplicative noise. A simple and effective method of smoothing speckle-corrupted images by a digital computer is discussed, based on the recently developed sigma filter. The sigma filter is motivated by the sigma probability of a Gaussian distribution. The pixel to be processed is replaced by an advantage of those neighboring pixels having their gray level within two noise standard deviations from that of the concerned pixel. Consequently the speckles are suppressed without blurring edges and fine detail. Several Seasat SAR images are used for illustration, and comparisons are made with several noise-smoothing algorithms. Extensions of this algorithm to contrast enhancement and signal-dependent noise filtering are also presented. This algorithm is computationally efficient, and has the potential to achieve real or near real-time processing.