Huo et al. 16 comrades were awarded the honorary title of "Jiamusi Youth May 4th Medal", Lu Binghai et al. 10 comrades were awarded the honorary title of "Top Ten Outstanding Youth in Jiamusi City", and Zhou et al. 7 comrades were awarded the nomination prize of "Top Ten Outstanding Youth in Jiamusi City". Zhao chunhui
Thesis title: Research on the theory and algorithm of digital morphological filter.
About the author: Zhao Chunhui, male, born in 1965, studied under Professor Sun of Harbin Institute of Technology in 1994, and received his doctorate in 1998.
abstract
This project is supported by the National Natural Science Foundation of China and international cooperation projects. Digital morphological filter is a very important nonlinear filter. It is widely used in image analysis and processing, computer vision and pattern recognition, and is a research hotspot in the field of nonlinear digital signal processing.
With the development of modern digital signal processing technology, nonlinear digital signal processing methods play an increasingly important role in the field of signal processing, because a large number of signal processing problems in natural phenomena and social phenomena are nonlinear. Although the linear digital signal processing method is mature in theory and simple to implement, its processing results for nonlinear problems are not ideal in most cases. In recent twenty years, great progress has been made in nonlinear digital signal processing technology, including the research on nonlinear digital filters.
Filtering noise signal (image) is one of the basic tasks of signal (image) processing. In the past, this task was mainly accomplished by linear filter, but linear filter can not effectively suppress all kinds of non-additive Gaussian noise, and it is not conducive to the maintenance of detailed features such as signal edges. Therefore, in recent years, the problem of noise signal recovery is mainly dealt with by nonlinear filters. Among many nonlinear filters, morphological filter is the most representative and promising one, because it is based on mathematical morphology and has the characteristics of parallel and fast implementation, which has been widely concerned and studied by scholars at home and abroad. Morphological filter is a new type of nonlinear filter developed from mathematical morphology. Morphological filtering theory was founded by G. Matheron and J. Serra in the early 1980s. Morphological filtering is based on the geometric structure characteristics of the signal (image), and uses predefined structural elements (equivalent to the filtering window) to match or locally correct the signal, so as to extract the signal and suppress the noise.
Morphological filter is developed with the development of mathematical morphology. From the earliest binary morphological filter to the later multivalued morphological filter. Multi-valued morphological filter is closely related to sorting statistical filter, which is essentially a special case of overlapping filter. When the horizontal organization element is used, the multi-valued expansion and corrosion transformation evolves into maximum and minimum filtering. The maximum filter can usually effectively filter out the negative impulse noise in the image, and the minimum filter can filter out the positive impulse noise, but both of them are ineffective for mixed impulse noise. If various cascade combinations of the two are adopted, more comprehensive impulse noise suppression performance can be obtained.
Due to the complexity and diversity of nonlinear filter theory and algorithm, morphological filter has not yet formed a systematic design method. Most of the existing algorithms are aimed at a practical need, lack of in-depth theoretical analysis, and have limitations in application. The research in this field is not deep enough and perfect, and there is still a lot of work to be done. The research on the theory and algorithm of morphological filtering in China started late, and the research level is relatively backward. In order to track the international frontier in this field, develop the nonlinear digital signal processing technology in China, and meet the needs of aerospace, national defense and national economy, it is necessary and realistic to deeply study the theory and application technology of morphological filtering.
The performance of morphological filters depends on the structural elements and the types of morphological transformations. How to choose them reasonably, construct fast algorithms with good performance and make in-depth theoretical analysis is a difficult problem in this research field. In this paper, the basic theory of morphological filters is studied, and the principles, structures and algorithms of several morphological filters are systematically studied by using serial or parallel, linear weighted combination and adaptive processing methods. The main research contents and achievements of this paper include the following aspects:
1. Summarizes the basic theory of digital morphological filter systematically and comprehensively. Based on the signal state model method and overlapping filter description method, the root signal characteristics and output statistical characteristics of traditional morphological filters (including morphological open filter, closed filter, open-close filter and closed-open filter) are emphatically studied, the relationship between the root signals of the above filters is pointed out, and the serious statistical deviation of the output of traditional morphological filters is expounded, which is the direct reason that affects its noise filtering effect. In addition, through the parallel and serial combination of traditional morphological filters, this paper successfully applies morphological filtering method to the restoration of noisy ECG waveform and the extraction of two-dimensional image targets.
2. In order to reduce the statistical deviation of traditional morphological open-closed and closed-open filters, this paper proposes a new type of filters-generalized morphological open-closed (GOC) and closed-open (GCO) filters by using two structural elements with different sizes, and proves that these filters satisfy the four basic properties of morphological transformation (translation invariance, monotonicity, duality and idempotency). In order to better understand their filtering process, this paper analyzes the root signal characteristics of generalized morphological filters based on the above signal state model method. With the help of the description of positive Boolean function (PBF), the generalized morphological filter is represented as an overlapping filter. Based on the output statistical characteristics of cascaded filters, the analytical expressions of the output functions of generalized open-closed and closed-open filters under the condition of one-dimensional convex structural elements are derived, the output statistical laws of such filters under three common input noise distributions (uniform, Gaussian and double exponential) are analyzed, and their digital characteristics (mean and variance) are calculated. In addition, on the basis of generalized open-closed and closed-open filters, an adaptive weighted combined generalized morphological filter is proposed by using adaptive method, which is verified by one-dimensional and two-dimensional signal simulation and satisfactory results are obtained.
3. Based on the multi-template matching method, linear multi-structural elements are introduced into the generalized open-closed and closed-open filters, and a class of parallel composite generalized morphological filters with multi-structural elements is defined. The constrained minimum mean square error (CLMS) algorithm is used to study the adaptive weighted average generalized morphological filtering algorithm with multiple structural elements. The simulation results verify the effectiveness of the above filtering algorithm.
4. Based on the concept of omni-directional structural elements, the maximum open operation and minimum closed operation are defined, and on this basis, they are cascaded in different order to construct a class of omni-directional multistage combined filters. Finally, an omni-directional multi-level weighted combined morphological filtering method is proposed by using the weighted average operation of morphological transformation. The computer simulation results show that this method has good performance in suppressing noise and maintaining the geometric characteristics of signals.
5. The optimization of sequential morphological filtering is studied. Firstly, the statistical characteristics of the output of the sequential morphological filter are analyzed, and the influence of percentile value and structural elements on the filtering performance is pointed out. Aiming at the limitation of the application of fixed parameter filter, adaptive LMS algorithm is used to realize the adaptive processing of percentile value and structural elements under the criterion of mean square error and average absolute error. This filter can be used to filter out the step signal containing noise (including mixed impulse noise).
This paper not only made a great breakthrough in theory, but also published more than 20 papers with academic value, and many papers were retrieved and included by international authoritative journals, which has important academic significance; The research results have been applied in practical engineering projects and achieved remarkable economic benefits.
The research results of this topic have important academic value for enriching the knowledge of nonlinear digital signal processing, and have important guiding significance and reference value for the research and development of other types of nonlinear filters, especially for the development of image processing, pattern recognition and computer vision. Its achievements will have a wide application prospect in the fields of aerospace remote sensing, image matching terminal guidance, artificial intelligence, robot vision, biomedicine, earthquake and sonar signal processing.
Key words: mathematical morphology, morphological filter, structural elements, nonlinear filtering, image processing.
Research on the Theory and Algorithm of Digital Morphological Filtering
Dissertation of Harbin Institute of Technology
Author: Zhao Chunhui
abstract
This project is supported by the National Science Foundation and international cooperation projects. Digital morphological filter is an important nonlinear filter. It is widely used in many research fields such as image analysis and processing, computer vision and pattern recognition. At present, it is a hot spot of nonlinear research in digital signal processing.
With the development of modern digital signal processing technology, nonlinear digital signal processing methods become more and more important in the field of signal processing, because there are a lot of nonlinear problems in natural and social phenomena. Although the linear digital signal processing method is mature in principle and easy to realize, in most cases, the processing effect of nonlinear problems is not very ideal. In recent 20 years, great progress has been made in nonlinear digital signal processing technology, such as the research of nonlinear digital filter.
Filtering noise signal (or image) is one of the basic signal processing tasks. In the past, this task was mainly accomplished by linear filters. However, the linear filter can not effectively suppress all kinds of Gaussian white noise, and keep the detailed features such as the edge of the signal. Therefore, in recent years, nonlinear filters have solved the problem of noise signal recovery. Morphological filter is one of the representative and promising nonlinear filters. Because it is based on mathematical morphology (MM) and can be implemented in parallel. Some scholars at home and abroad have paid extensive attention to and studied this issue. Morphological filter is a new type of nonlinear filter derived from mathematical morphology. Morphological filtering theory was founded by G. Matheron and J. Serra in the early 1980s, and it is based on the geometric structure characteristics of signals (or images). In order to collect signals and suppress noise, morphological filters match or locally modify signals through predefined structural elements (filtering windows).
Morphological filter is developed with mathematical morphology. It is evaluated from binary 1 to grayscale 1. Gray morphological filter is closely related to sequential statistical filter. Both of them are essentially a kind of laminated filter. When plane structural elements are used, gray expansion and corrosion evolve into maximum and minimum filtering. Usually, the maximum filter can filter out negative impulse noise, and the minimum filter can effectively filter out positive impulse noise. However, neither method is suitable for mixed impulse noise. If all of them are connected in series, the ability to suppress all kinds of impulse noise can be obtained.
Because of the complexity and diversity of nonlinear filter theory and algorithm, there is no systematic method to design morphological filter. Most of the existing algorithms are put forward according to certain actual needs, lacking in-depth theoretical analysis, and have certain limitations in application. This research is not thorough, and there is still a lot of work to be done in this field. The research on morphological filtering theory and its algorithm started late in China. In order to follow the international frontier, develop the nonlinear digital signal processing technology in China, and further study the morphological filtering theory and practical technology to meet the needs of aerospace, national defense and economic development, it is very necessary and realistic.
The performance of morphological filter depends on its structural elements and the type of morphological transformation. The reasonable selection of morphological filters, the construction of fast algorithms with good performance and in-depth theoretical analysis are still difficult problems. Based on the basic theory of morphological filter, this paper focuses on the selection of structural elements and the combination of morphological transformation, and systematically studies the principle, structure and algorithm of morphological filter by means of serial/parallel processing, linear weighted combination and adaptive processing. The main contents and contributions of this paper are as follows:
1. This paper systematically and comprehensively summarizes the basic theory of digital morphological filters. On the basis of signal state modeling and cascade filter description, this paper studies the root signal characteristics and output statistical characteristics of traditional morphological filters (including open, closed, open-closed and closed-open), clarifies the relationship between various root signals of the above filters, and points out that the statistical deviation in the output of traditional morphological filters is the direct reason for its low denoising efficiency. In addition, morphological filtering method has been successfully applied to waveform recovery of noisy ECG signals and geometric shape extraction of objects in two-dimensional images.
2. In order to reduce the statistical deviation of the output of traditional open-closed and closed-open filters, this paper proposes a new class of generalized open-closed (GOC) and closed-open (GCO) filters by using two structural elements with different sizes, and proves that these filters have four basic properties (translation invariance, monotonicity, duality and idempotency). In order to better understand the filtering process of generalized morphological filter, this paper analyzes the root signal characteristics of generalized morphological filter on the basis of the above signal state modeling method. With the help of the description of positive Boolean function (PBF), the generalized morphological filter is represented as a cascade filter. Based on the statistical characteristics of stacked filters, the analytical expressions of output functions of GOC and GCO filters with one-dimensional convex structural elements are derived. We analyzed the statistical law of this kind of filter and calculated the digital characteristics (mean and variance). In addition, based on GOC/ GCO filtering and adaptive processing methods, an adaptive weighted combined generalized morphological filter is proposed. The simulation results of one-dimensional and two-dimensional signals are satisfactory.
3. Based on the multi-template matching method, linear multi-structural elements are introduced into GOC and GCO filters, and the definition of parallel composite generalized morphological filter is given. In addition, the generalized algorithm of adaptive weighted average is studied by using the constrained least mean square (CLMS) error method. The simulation results show that the above filtering algorithm is effective.
4. In this paper, we define a class of maximum opening and minimum closing operations based on omni-directional structural elements, and further construct a class of omni-directional multilevel combinational morphological filters through their difficult level association. Finally, through the weighted average operation of morphological transformation, an omni-directional multi-level weighted combined morphological filtering algorithm is proposed. Computer simulation results show that the algorithm has good noise suppression and geometric feature preservation performance.
5. The optimization of ordered morphological filtering is studied. It is pointed out that structural elements and percentiles have influence on the filtering results. Aiming at the limitation of fixed parameter filter, under the criteria of mean square error (MSE) and mean absolute error (MAE), this paper adopts adaptive LMS algorithm to realize the adaptive processing of percentile and structural elements in sorting morphological filtering. These filters have important applications in filtering noise step change signals.
The research results of this paper have published more than 20 papers with academic value. In addition, many papers are included in international authoritative indexes and abstracts. They are of great academic significance. This paper not only makes great progress in theory, but also has important applications in practical engineering projects. There are many remarkable economic benefits.
The research results of this paper have important academic value for enriching the field of nonlinear digital signal processing, and also have guiding significance for developing other nonlinear filters. In particular, it has a positive impact on promoting the development of image processing, computer vision and pattern recognition. They are widely used in aerospace remote sensing, image matching guidance, artificial intelligence, robot vision, biomedicine, earthquake and sonar signal processing.
Keywords: mathematical morphology, morphological filter, structural elements, nonlinear filtering, image processing