Typically, the region of interest (ROI), in the JPEG2000 standard, is manually defined, and then wavelets are used to compress the ROI at a higher bitrate than the rest of the image. The wavelet decomposition in JPEG2000 also lends itself to texture and edge extraction for segmentation and classification purposes. In this paper, a semi-automatic ROI generation algorithm for images is presented, where the texture and edge information provided by the first level of the wavelet decomposition is used to segment the wavelet coefficients. This first-level decomposition provides enough edge and texture information for image segmentation, allowing computational savings. A mask that outlines the ROI is determined based on the entropy calculation of the segmented regions. The advantage of this method is that the segmentation process is entirely performed in the wavelet and not in the pixel domain, therefore offering additional computational efficiency. The resulting ROI is coded using the MAXSHIFT method. The algorithm was applied and successfully demonstrated in several images.
An adaptive discrete cosine transform (DCT) algorithm was presented by Hontsch et. al. under the perceptual metric which provided good bit rate. However, this method requires carefully calibrated viewing conditions. In this paper, we present a new adaptive discrete cosine transform where the quantization steps are adapted for each DCT coefficient using the new universal quality index. This new quality index does not require carefully calibrated viewing conditions and it is based on a combination of luminance and contrast distortions, and loss of correlation. Results obtained show
that the procedure converges and provides a good bit rate.
In our previous literature, we proposed a class of nonlinear filters whose output is given by a linear combination of weighted medians (LCWM) of the input sequence. We showed that, unlike the median type filters having the lowpass response, the LCWM filters consisting of weighted median subfilters can not only suppress both Gaussian noise and impulsive noise effectively, but also offer various frequency characteristics including lowpass, bandpass, and highpass responses. In an attempt to improve the performance of LCWM filters, we propose an adaptive LCWM (ALCWM) filter which consists of directional weighted median subfilters with different geometric structures. The weighting factor of each subfilter is adaptively determined using the similarity between the directional subwindow and the local geometric image features of interest. It is shown experimentally that the ALCWM filter performs better than the aforementioned filters including the median and the LCWM filters in preserving more details.
In this paper, we propose a frequency selective weighted median (FSWM) filter with arbitrary spectral behavior. The proposed scheme is motivated by the observation on the structure and design procedure of the linear-phase FIR high- pass (HP) filter. An FIR HP filter can be easily obtained by changing the sign of coefficients in odd position. Thus, the output of the HP filter can be represented as the difference between two subfilters which have all positive coefficients. This representation structure of the FIR HP filter is analogous to the difference of estimates (DoE) such as the difference of medians (DoM). The DoM is essentially a robust HP filter which is commonly used in edge detection. Based on this observation, we define a new nonlinear filtering structure consisting of linear combinations of weighted medians. We refer to this new filter class as the FSWM filter. It is shown experimentally that the FSWM filter can offer 'low-pass (LP),' 'HP,' 'band-pass (BP),' and 'band-stop (BS)' frequency characteristics.
Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities, is used to compare the behavior of linear and non-linear filters. In the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this difficulty is the highly non-linear nature of the partitions and generating function used. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented in not completely refined, it certainly appears to be promising. Some results will be shown.
KEYWORDS: Chemical elements, Algorithm development, Electronic filtering, Multiscale representation, Image filtering, Image processing, Signal to noise ratio, Seaborgium, Signal processing, Linear filtering
Recent papers in multiscale morphological filtering, particularly, have renovated the interest in signal representation via multiscale openings. Although most of the analysis was done with flat structuring elements, extensions to grayscale structuring elements (GSE) are certainly possible. In fact, we have shown that opening a signal with convex and symmetric GSE does not introduce additional zero-crossings as the filter moves to a coarser scales. However, the issue of finding an optimal GSE is still an open problem. In this paper, we present a procedure to find an optimal GSE under the least mean square (LMS) algorithm subject to three constraints: The GSE must be convex, symmetric, and non-negative. The use of the basis functions simplifies the problem formulation. In fact, we show that the basis functions for convex and symmetric GSE are concave and symmetric, thus alternative constraints are developed. The results of this algorithm are compared with our previous work.
This paper presents a fast implementation method for grayscale function processing (FP) systems. The proposed method is based on the matrix representation of the FP system using the basis matrix (BM) and the block basis matrix (BBM). The computational efficiency derives from recursive algorithms based on some characteristics of the BM and BBM matrices. It is shown that, with the proposed scheme, both opening and closing can be determined in real time by 2N - 2 additions and 2N - 2 comparisons, and open-closing and close-opening by 4N - 4 additions and 4N - 4 comparisons, when the size of the GSE is equal to N.
In this paper, we expand the statistical properties of grayscale compound function processing (FP) morphological operators. This is achieved by utilizing the basis matrix representation which is an extension of the basis function theorem. It is shown that the basis matrix is skew symmetric and this fact is highly exploited in finding the output density functions of grayscale opening and closing. The proposed method is also applicable to function set processing operators since these operators are a special case of the FP operators.
In this paper, we introduce a method to design gray scale composite morphological operators as fuzzy neural networks. In this structure, synaptic weights are represented by a gray scale structuring element. The proposed method is a two-step procedure. First, a suitable neural topology is found through the basis functions of the composite operators. Second, a learning rule based on the average least mean square is applied where each synaptic weight is found through a back propagation algorithm. One dimensional examples are shown. This scheme can be easily extended to two dimensions.
This paper introduces a neural network implementation of gray scale operators. In this structure, synaptic weights are represented by a gray scale structuring element and trained by a learning algorithm based on an optimal criterion called the overall equality index. The proposed algorithm leads to a computationally simple implementation, with numerical examples to illustrate its performance.
The aim of this paper is to find a relationship between alternating sequential filters and the morphological sampling theorem developed by Haralick. First, we show an alternative proof for opening and closing in the sampled and unsampled domain. This is done by using basis functions. This decomposition is used then to show the relationship of opening- closing in the sampled and unsampled domain. An upper and a lower bound, for the previous relationships, were found. Under certain circumstances, an equivalence is shown for opening-closing between the sampled and the unsampled domain. An extension to more complicated algorithms is also considered, namely; union of openings and intersection of closings. The reason to consider such transformations is that in some applications we would like to eliminate pixels removed by individual openings (closings).
Mathematical Morphology is a new branch of mathematics powerful enough to study some vision problems like multiscale filtering. Due to the fact morphological openings smooth the signal while preserving the edges, and using the three Matheron's axioms, an important result is obtained: morphological openings do not introduce additional zero-crossing as one moves to a coarser scales. With these results a multiscale filtering scheme is developed. The choice of the structuring element is constrained to the sub-space of convex, compact and homothetic ones. In this paper we will report a procedure for choosing the structuring element based on the pre-filtering effects of morphological openings and the subsequent detection of edges.
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