Qiaofei Wang

Root properties of morphological filters

Abstract The characterization of the root signal sets of the most common digital morphological filters is presented in this paper. This has proven very crucial in understandinng the utility and usefulness of these nonlinear operators. Important deterministic properties of root signals of morphological opening, closing, open-closing and clos-opening are derived leading to a complete characterization of output signals. Recall that the output signals of these morphological filters are root signals since the filters are idempotent. A system of difference equations is then derived to compute the number of root signals for these morphological filters by a structuring element of width k and for signals of length n with m quantization levels. The derivation is based on the state description for these root signals. Simplified recursive equations have been obtained for binary root signals. An application example where the root signals are used in block truncation coding (BTC) for image compression is discussed.

Adaptive grayscale morphological filters for image noise smoothing

The authors find an optimal solution for designing a gray-scale morphological filter. An adaptive algorithm is developed for determining, from a given class of gray-scale morphological filters, a filter which minimizes the mean square error between its output and a desired process. The adaptation using the conventional least mean square algorithm optimizes the gray-scale structuring element in a given search area. The noise removal performance is compared to that of another class of nonlinear filters, i.e., adaptive and nonadaptive stack-based filters.<<ETX>>

BTC image coding using two-dimensional median filter roots

Application of root signals of two-dimensional median filters to BTC (block truncation coding) is investigated. The 2D median filters considered are the 3*3 separable median (SM) filter and the 5-point cross window median (CWM) filter, as these two types of filters preserve image details well. Some properties of the root signal sets of these two filters are studied. It is shown that using the root signals of SM or CWM filters to perform BTC coding, little degradation results in the coded images, whereas the bits/pixel needed reduce to 1.69 or 1.81, respectively, compared to the standard BTC coding method whose bits/pixel are 2.0.<<ETX>>

Deterministic properties of separable and cross median filters with an application to block truncation coding

In this paper, we present some deterministic properties of separable and cross median filters. It is proved that in the absence of vertical binary oscillations, the roots of a separable median filter are included in a subset of root signals of the corresponding cross median filter. Moreover, the sufficient and necessary condition is given for a point to be invariant to cross median filtering. On the root structures of cross median filters, we indicate that there exist three different types of regions based on the one-dimensional features of rows and columns. Finally, an application example is discussed where the roots of separable and cross median filters are used in block truncation coding (BTC) for image compression.

State description for the root signal sets of morphological filters

The root signal sets of the basic morphological filters are characterized. Several properties of these root signals are studied and used as the basis for a state model for the root signal set. The model leads to simple recursive equations that can be used to compute the total number of root signals for arbitrary length structuring elements.<<ETX>>

BTC image coding using mathematical morphology

The application of mathematical morphology to block truncation coding (BTC) image coding is investigated. First the overhead statistical information, namely, sample mean and sample variance, are encoded using the DPCM technique with adaptive morphological predictors. Then the authors propose utilizing the roots of morphological filters to compress the bits for the bit plane. Compared to the standard BTC coding method, the bits/pixel needed are reduced according to the local statistics of an image. The results were comparable to or slightly better than the results obtained by a median-based BTC image coding scheme.<<ETX>>

Application of median-type filtering to image segmentation in electrophoresis

In order to extract the protein spots in a gel image from the uneven background which has sharp edges, e.g., lines and streaks in some areas, the authors have developed a detection algorithm where the median, FMH or morphological filter is taken as the smoother to estimate the varying background. The performance comparison shows that FMH detectors provide a simple implementation as well as a good compromise between streak removing and spot distortion.

Deterministic and statistical properties of two-dimensional FIR-median hybrid filters

In this paper, we present a new class of two-dimensional FIR-median hybrid (FMH) filters, which we call separable FMH filters, for image noise smoothing. In a separable FMH filter, a one-dimensional FMH filter is applied to the rows and the columns of an image successively. The deterministic properties of separable and cross window FMH filters are discussed. Under certain assumptions, it is proved that a root of a separable FMH filter is a root of the corresponding cross window FMH filter. The noise attenuating properties of a separable FMH filter are studied and compared with those of the separable median filter, the two-dimensional median filter with a square window, and the cross window FMH filter.

Root-signal sets of morphological filters and their use in variable-length BTC image coding

The characterization of the root-signal set of a nonlinear operator has proved to be a crucial step in understanding the utility and usefulness of the operator. The set of root signals constitutes the passband of the nonlinear operator, and the complement of this set represents the stopband of the operator. Knowledge of these two sets for all operators determines which one must be used for any particular task. In this paper we investigate the root signals of the basic morphological filters, we study the properties of these signals, and we derive a system of equations to compute the number of binary-root signals for these morphological filters with structuring element of width k and signals of length n. The derivation is based on the state description for these root signals. Simple recursive equations are derived for counting the number of root signals of opening, closing, open-closing, and clos-opening. An application example in which these root signals are used in block truncation coding for image compression is discussed.

Adaptation of gray-scale morphological filters

Grayscale morphology has been widely used in image processing, especially in noise removal. In this paper, we find an optimal solution for designing a grayscale morphological filter. An adaptive algorithm is developed for determining, from a given class of grayscale morphological filters, a filter which minimizes the mean square error between its output and a desired process. The adaptation using the conventional least mean square algorithm optimizes the grayscale structuring element in a given search area. The performance of noise removal is compared to another class of nonlinear filters, i.e., adaptive and nonadaptive stack-based filters.