ããå¨æå¸å¬å¼çå
±éå¢çºªå¿µâäºåâè¿å¨87å¨å¹´æ¨å
è¿éä½ãä¼ç§ä¸ªäººè¡¨å½°å¤§ä¼ä¸ï¼ä¸æ¹åäºåé ãçäºå¥ç®çæ¶ä»£éå¹´åå°è¡¨å½°å¥å±ã
ããééæç16ååå¿è¢«æäºâä½³æ¨æ¯å¸éå¹´äºåå¥ç« âè£èªç§°å·ï¼å¢ä¸æµ·ç10ååå¿è¢«æäºç¬¬ä¹å±âä½³æ¨æ¯å¸å大æ°åºéå¹´âè£èªç§°å·ï¼å¨ä¿é¾ç7ååå¿è¢«æäºâä½³æ¨æ¯å¸å大æ°åºéå¹´âæåå¥ãèµµæ¥æ
ãã论æé¢ç®ï¼æ°åå½¢æ滤波å¨ç论åå
¶ç®æ³ç 究
ããä½è
ç®ä»ï¼èµµæ¥æï¼ç·ï¼1965å¹´çï¼1994å¹´å¸ä»åå°æ»¨å·¥ä¸å¤§å¦åå£åææï¼äº1998å¹´è·å士å¦ä½ã
ããæ è¦
ããæ¬è¯¾é¢æ¯å½å®¶èªç¶ç§å¦åºéèµå©åå½é
åä½é¡¹ç®ãæ°åå½¢æ滤波å¨æ¯ä¸ç§é常éè¦çé线æ§æ»¤æ³¢å¨ãå®å¨å¾è±¡åæä¸å¤çã计ç®æºè§è§å模å¼è¯å«çé¢åè·å¾äºå¹¿æ³çåºç¨ï¼æ¯ç®åé线æ§æ°åä¿¡å·å¤çå¦ç§ç 究ççç¹è¯¾é¢ã
ããéçç°ä»£æ°åä¿¡å·å¤çææ¯çåå±ï¼é线æ§æ°åä¿¡å·å¤çæ¹æ³å¨ä¿¡å·å¤çé¢åä¸çå°ä½åä½ç¨æ¾å¾è¶æ¥è¶éè¦ï¼å 为ä»èªç¶ç°è±¡å社ä¼ç°è±¡ä¸æ¶ç°åºæ¥ç大éä¿¡å·å¤çé®é¢æ¯é线æ§çã线æ§æ°åä¿¡å·å¤çæ¹æ³è½ç¶å¨ç论ä¸æ¯è¾æçï¼ä¸å®ç°ç¸å¯¹ç®åï¼ä½å®å¯¹é线æ§é®é¢çå¤çç»æå¨å¤§å¤æ°æ
åµä¸æ¯ä¸ååçæ³çãè¿äºåå¹´æ¥ï¼é线æ§æ°åä¿¡å·å¤çææ¯å·²åå¾äºé¿è¶³è¿å±ï¼å
¶ä¸å
æ¬å¯¹é线æ§æ°å滤波å¨çç 究ã
ããåªå£°ä¿¡å·(å¾è±¡)ç滤波æ¯ä¿¡å·(å¾è±¡)å¤ççåºæ¬ä»»å¡ä¹ä¸ãè¿å»è¿ä¸ä»»å¡ä¸»è¦ç±çº¿æ§æ»¤æ³¢å¨æ¥å®æï¼ä½çº¿æ§æ»¤æ³¢å¨ä¸è½ææå°æå¶åç§éå æ§é«æ¯åªå£°ï¼ä¸ä¸å©äºä¿¡å·è¾¹ç¼çç»èç¹å¾çä¿æï¼å èï¼è¿å¹´æ¥çåªå£°ä¿¡å·æ¢å¤é®é¢ä¸»è¦éç¨é线æ§æ»¤æ³¢å¨æ¥å¤çãå¨è¯¸å¤ç§ç±»çé线æ§æ»¤æ³¢å¨ä¸ï¼å½¢æ滤波å¨æ¯æå
·ä»£è¡¨æ§åå¾æåå±åéçä¸ç§æ»¤æ³¢å¨ï¼å 为å®æ¯ä»¥æ°å¦å½¢æå¦ä¸ºç论åºç¡ï¼å
·æ并è¡å¿«éå®ç°çç¹ç¹ï¼ä¸ç´åå°äºå½å
å¤å¦è
çæ®éå
³æ³¨å广æ³ç 究ãå½¢æ滤波å¨æ¯ä»æ°å¦å½¢æå¦ä¸åå±åºæ¥çä¸ç±»æ°åé线æ§æ»¤æ³¢å¨ãå½¢æ滤波ç论æ¯ç±G. Matheron åJ. Serraç人å¨å
«å年代ååç«çãå½¢æ滤波å¨æ¯åºäºä¿¡å·(å¾è±¡)çå ä½ç»æç¹æ§ï¼å©ç¨é¢å
å®ä¹çç»æå
ç´ (ç¸å½äºæ»¤æ³¢çª)对信å·è¿è¡å¹é
æå±é¨ä¿®æ£ï¼ä»¥è¾¾å°æåä¿¡å·ï¼æå¶åªå£°çç®çã
ããå½¢æ滤波å¨æ¯ä¼´éçæ°å¦å½¢æå¦çåå±èåå±çï¼å®ç±ææ©çäºå¼å½¢æ滤波å¨åå±ä¸ºåæ¥çå¤å¼å½¢æ滤波å¨ãå¤å¼å½¢æ滤波å¨ä¸æåºç»è®¡æ»¤æ³¢å¨æçå¯åçèç³»ï¼å®ä»¬æ¬è´¨ä¸æ¯å±è¿æ»¤æ³¢å¨çç¹æ®æ
åµãå½éç¨å¹³ç»æå
ç´ æ¶ï¼å¤å¼çè¨èåè
èåæ¢å°±æ¼å为æ大åæå°æ»¤æ³¢ãæ大滤波å¨é常è½ææå°æ»¤é¤å¾è±¡ä¸çè´èå²åªå£°ï¼èæå°æ»¤æ³¢å¨å¯ä»¥æ»¤é¤æ£èå²åªå£°ï¼ä½ä¸¤è
å对混ååèå²åªå£°å¤±æãå¦æéç¨ä¸¤è
çåç§çº§èç»åï¼åå¯è¾¾å°è¾å
¨é¢çèå²åªå£°æå¶æ§è½ã
ããç±äºé线æ§æ»¤æ³¢å¨ç论åç®æ³çå¤ææ§ãå¤æ ·æ§ï¼å½¢æ滤波å¨è³ä»å°æªå½¢æç³»ç»ç设计æ¹æ³ãç°æçç®æ³å¤§å¤æ¯é对æä¸å®é
éè¦æåºæ¥çï¼ç¼ºä¹æ·±å
¥çç论åæï¼ä¸åºç¨ä¹åå¨çå±éæ§ãè¿ä¸é¢åçç 究è¿å¾ä¸æ·±å
¥åå®åï¼è¿æ大éå·¥ä½éè¦æ¥å®æãæå½å¯¹å½¢æ滤波ç论åç®æ³çç 究起æ¥è¾æï¼å
¶ç 究水平ä¹è¾ä¸ºè½åã为äºè·è¸ªè¯¥é¢åå½é
å沿ï¼åå±æå½é线æ§æ°åä¿¡å·å¤çææ¯ï¼æ»¡è¶³èªå¤©ãå½é²åå½æ°ç»æµå¯¹è¯¥ææ¯çéæ±ï¼è¿ä¸æ¥å¼å±å½¢æ滤波ç论ä¸åºç¨ææ¯ç 究æ¯é常å¿
è¦èæå®é
æä¹çã
ããå½¢æ滤波å¨çæ§è½åå³äºç»æå
ç´ åå½¢æåæ¢çç±»åï¼å¦ä½åçå°éæ©å®ä»¬ï¼æé æ§è½è¯å¥½çå¿«éç®æ³ï¼å¹¶å¯¹å
¶è¿è¡è¾æ·±å
¥çç论åæï¼æ¯è¯¥ç 究é¢åä¸çä¸ä¸ªé¾é¢ãæ¬æä»ç 究形æ滤波å¨çåºæ¬ç论å
¥æï¼å´ç»çç»æå
ç´ çéååå½¢æåæ¢çç»åè¿ä¸ä¸»é¢ï¼éè¿éç¨ä¸²è¡æ并è¡ã线æ§å æç»ååèªéåºå¤ççæ¹æ³ï¼ç³»ç»å°ç 究äºå ç§å½¢æ滤波å¨çåçãç»æåç®æ³ãæ¬æç主è¦ç 究å
容ååå¾çææå
æ¬å¦ä¸å 个æ¹é¢ï¼
ãã1. ç³»ç»èè¾å
¨é¢å°æ»ç»äºæ°åå½¢æ滤波å¨çåºæ¬ç论ã åºäºä¿¡å·ç¶æ模åæ³åå±è¿æ»¤æ³¢æè¿°æ³ï¼æ¬æéç¹ç 究äºä¼ ç»å½¢æ滤波å¨(å
æ¬å½¢æå¼æ»¤æ³¢å¨ãé滤波å¨ãå¼âé滤波å¨åéâå¼æ»¤æ³¢å¨)çæ ¹ä¿¡å·ç¹æ§åè¾åºç»è®¡ç¹æ§ï¼æåºäºä¸è¿°å类滤波å¨æ ¹ä¿¡å·é´çå
³ç³»ï¼å¹¶éæäºä¼ ç»å½¢æ滤波å¨çè¾åºåå¨ç严éçè¾åºç»è®¡ååç°è±¡ï¼è¿æ¯å½±åå®ä»¬åªå£°æ»¤æ³¢ææçä¸ä¸ªç´æ¥åå ãå¦å¤ï¼éè¿ä¼ ç»å½¢æ滤波å¨ç并è¡å串è¡ç»åï¼æ¬æå°å½¢æ滤波æ¹æ³æåå°åºç¨äºå«åªå£°å¿çµä¿¡å·æ³¢å½¢çæ¢å¤åäºç»´å¾è±¡ç©ä½çæåã
ãã2. 为äºåå°ä¼ ç»å½¢æå¼âéåéâå¼æ»¤æ³¢å¨è¾åºç»è®¡ååï¼æ¬æéç¨ä¸¤ä¸ªä¸å尺寸ç»æå
ç´ ï¼æåºäºä¸ç±»æ°åç滤波å¨â广ä¹å½¢æå¼âé(GOC)åéâå¼(GCO)滤波å¨ï¼å¹¶è¯æäºè¿ç±»æ»¤æ³¢å¨æ»¡è¶³å½¢æåæ¢çå个åºæ¬æ§è´¨(平移ä¸åæ§ãåè°æ§ã对å¶æ§åå¹çæ§)ã为äºæ´å¥½å°äºè§£å®ä»¬æ»¤æ³¢è¿ç¨ï¼æ¬æåºäºä¸è¿°çä¿¡å·ç¶æ模åæ³ï¼åæäºå¹¿ä¹å½¢æ滤波å¨çæ ¹ä¿¡å·ç¹æ§ãåå©äºæ£å¸å°å½æ°(PBF)çæè¿°ï¼å°å¹¿ä¹å½¢æ滤波å¨è¡¨ç¤ºæä¸ç§å±è¿æ»¤æ³¢å¨ãéè¿å±è¿æ»¤æ³¢å¨çè¾åºç»è®¡ç¹æ§ï¼æ们æ¨å¯¼åºäºå¹¿ä¹å¼âéåéâå¼æ»¤æ³¢å¨å¨ä¸ç»´å¸ç»æå
ç´ æ
åµä¸çè¾åºå½æ°è§£æ表达å¼ï¼å¹¶å¨ä¸ç§å¸¸è§è¾å
¥åªå£°åå¸(ååãé«æ¯ååææ°)æ¡ä»¶ä¸ï¼åæäºè¿ç±»æ»¤æ³¢å¨çè¾åºç»è®¡è§å¾ï¼åæ¶è®¡ç®äºå®ä»¬çæ°åç¹å¾(åå¼åæ¹å·®)ãå¦å¤ï¼åºäºå¹¿ä¹å¼âéåéâå¼æ»¤æ³¢å¨ï¼å©ç¨èªéåºæ¹æ³ï¼æ¬ææåºäºä¸ç§èªéåºå æç»å广ä¹å½¢æ滤波å¨ï¼å¹¶å¯¹å
¶è¿è¡äºä¸ç»´åäºç»´ä¿¡å·ä»¿çéªè¯ï¼åå¾äºä»¤äººæ»¡æçç»æã
ãã3. åºäºå¤æ¨¡æ¿å¹é
æ¹æ³ï¼æ¬æå°çº¿æ§å¤ç»æå
ç´ å¼å
¥å°å¹¿ä¹å¼âéåéâå¼æ»¤æ³¢å¨ä¸ï¼å®ä¹äºä¸ç±»å¤ç»æå
ç´ å¹¶è¡å¤å广ä¹å½¢æ滤波å¨ã并å©ç¨æ约æçæå°åæ¹è¯¯å·®ç®æ³(CLMS)ï¼ç 究äºä¸ç§å¤ç»æå
ç´ èªéåºå æå¹³å广ä¹å½¢æ滤波ç®æ³ã仿çç»æéªè¯äºä¸è¿°æ»¤æ³¢å¨ç®æ³çæææ§ã
ãã4. åºäºå
¨æ¹ä½ç»æå
ç´ çæ¦å¿µï¼æ¬æå®ä¹äºæ大å¼åæå°éè¿ç®ï¼å¨æ¤åºç¡ä¸ï¼éè¿å®ä»¬çä¸å顺åºçº§èç»åï¼æé åºäºä¸ç±»å
¨æ¹ä½å¤çº§ç»å滤波å¨ãæåï¼éç¨å½¢æåæ¢çå æå¹³åè¿ç®ï¼æåºäºä¸ç§å
¨æ¹ä½å¤çº§å æç»åå½¢æ滤波æ¹æ³ã并è¿è¡äºè®¡ç®æºä»¿çå®éªï¼ç»æ表æè¿ç§æ¹æ³å¨åªå£°æå¶åä¿¡å·å ä½ç¹å¾ä¿ææ¹é¢æè¾å¥½çæ§è½ã
ãã5. ç 究äºé¡ºåºå½¢æ滤波çä¼åé®é¢ãé¦å
åæäºé¡ºåºå½¢æ滤波å¨çè¾åºç»è®¡ç¹æ§ï¼æåºäºç¾åä½å¼åç»æå
ç´ å¯¹æ»¤æ³¢æ§è½çå½±åãé对åºå®åæ°æ»¤æ³¢å¨åºç¨çå±éæ§ï¼æ¬æéç¨èªéåºLMSç®æ³ï¼å¨åæ¹è¯¯å·®(MSE)åååå¹³åç»å¯¹è¯¯å·®(MAE)ååä¸ï¼å®ç°äºç¾åä½å¼åç»æå
ç´ çèªéåºå¤çãè¿ç±»æ»¤æ³¢å¨å¯å¨å«åªå£°(å
æ¬æ··åèå²åªå£°)é¶è·ååä¿¡å·ç滤波åºåè·å¾éè¦åºç¨ã
ããæ¬è®ºæä¸ä»
å¨ç论ä¸æè¾å¤§ççªç ´ï¼å表äºäºåå¤ç¯æå¦æ¯ä»·å¼ç论æï¼ä¸æå¤ç¯è®ºæ被å½é
æå¨æ£ç´¢ååç©æ¶å½ï¼å
·æéè¦çå¦æ¯æä¹ï¼èä¸å
¶ç 究ææå·²å¨å®é
å·¥ç¨é¡¹ç®ä¸è·å¾äºéè¦åºç¨ï¼åå¾äºæ¾èçç»æµæçã
ããæ¬è¯¾é¢çç 究ææ对丰å¯é线æ§æ°åä¿¡å·å¤çç¥è¯å®åºæé大çå¦æ¯ä»·å¼ï¼å¯¹ç 究åå¼åå
¶å®ç±»åçé线æ§æ»¤æ³¢å¨å
·æéè¦çæ导æä¹ååèä»·å¼ï¼ç¹å«å¯¹å¾è±¡å¤çã模å¼è¯å«å计ç®æºè§è§çå¦ç§çåå±äº§ç积æçå½±åãå
¶ææå°å¨èªç©ºãèªå¤©é¥æï¼å¾è±¡å¹é
æ«å¶å¯¼ï¼äººå·¥æºè½ï¼æºå¨äººè§è§ï¼çç©å»å¦ãå°éå声纳信å·å¤ççé¢åæ广æ³çåºç¨åæ¯ã
ããå
³é®è¯ï¼æ°å¦å½¢æå¦ï¼å½¢æ滤波å¨ï¼ç»æå
ç´ ï¼é线æ§æ»¤æ³¢ï¼å¾è±¡å¤çã
ããRESEARCH ON DIGITAL MORPHOLOGICAL FILTER THEORY AND ITS ALGORITHMS
ããThe Dissertation of Harbin Institute of Technology
ããAuthor: Zhao Chunhui
ããAbstract
ããThis subject is supported by national science foundation and an international collaboration project. Digital morphological filter is an important nonlinear filter. It has found wide applications in many research fields, such as image analysis and processing, computer vision and mode recognition. At present, it is a hot subject of nonlinear research in digital signal processing.
ããWith the developments of modern digital signal processing techniques, the methods of nonlinear digital signal processing are increasingly important in the field of signal processing because of a majority of nonlinear problems existing in natural and social phenomena. Although the methods of linear digital signal processing are mature in principle and they are easily implemented, the processing results to nonlinear problems are not very prefect in most cases. In recent 20 years, the techniques of nonlinear digital signal processing have made great progress such as researching on nonlinear digital filters.
ããThe filtering of noisy signals (or images) is one of basic signal processing tasks. In the past, the task is mainly finished by linear filters. But linear filters cannot suppress various Gauss white noises and preserve fine-details features such as the edges of signals effectively. Thus, the restoration problems of noisy signals are solved by nonlinear filters in recent years. Morphological filter is a representative and hopeful nonlinear filter in all kinds of them. Because it is based on Mathematical Morphology (MM), and it can be realized in parallel. It has been noticed and researched widely by some scholars from home or oversea. Morphological filter is a new type of nonlinear filter stemming from Mathematical Morphology. Morphological filtering theory is founded by G. Matheron and J. Serra in the early eighties. It is based on the geometrical-structural features of signals (or images). In order to achieve the aims of collecting signals and suppressing noises, Morphological filter is matched with or modifies locally the signals by the structuring elements (filtering window) defined in advance.
ããMorphological filter is developing with Mathematical Morphology. It is evaluated from binary one to grayscale one. The grayscale morphological filter has close connection with order statistic filter. Both of them are one of stack filters in essence. When adopted flat structuring elements, grayscale dilation and erosion evolve to maximum and minimum filtering. Usually the maximum filter can remove negative impulsive noise and the minimum filter can remove positive impulsive noise effectively. However, both of them invalidate to mixed impulsive noise. If using the all serial combinations of them, we can obtain the capability to suppress all kinds of impulsive noises.
ããThere is not a systematic method for morphological filter designing because of the complexion and diversity of nonlinear filter theory and algorithms. Most of existing algorithms are proposed in accordance with a certain practical requirement, lacking penetrating theoretical analysis and having limitation in their applications. The research is not deeper yet and there are a lot of work to do in this field. Our country initiate late in researching on morphological filter theories and it algorithms. In order to trace with international forward position and develop our countryâ techniques of nonlinear digital signal processing, it is very necessary and realistic that we research further on morphological filter theory and practical techniques to meet the needs of spaceflight, national defense and economy.
ããThe performances of morphological filters depend on the types of their structural elements and morphological transforms. The reasonable choice of morphological filters, the constructing of their good-functioned fast algorithms and deep theoretical analyzing for them are still difficult problems. Starting from the investigation of the fundamental theory of morphological filters and concentrating on the choice of structuring elements and the combinations of morphological transforms, this dissertation systematically researches the principles, structures and algorithms of morphological filters by using the methods of serial/parallel processing, linear weighted combination and adaptive processing. The main contents and contributions of this dissertation are as follows:
ãã1. The fundamental theory of digital morphological filters is systematically and completely summarized in this dissertation. On the basis of the methods of signal state modeling and stack filter description, this dissertation researches the root signal characteristics and output statistical properties of traditional morphological filters (including opening, closing, open-closing and clos-opening), and illustrates the relationship between various root signals of above filters and points out that the phenomena of statistical biasing existing in the outputs of traditional morphological filters is the direct reason for their noise-removing efficiencies. In addition, the morphological filtering methods have successfully applied in the waveform restoration of noisy ECG signal and the extraction of geometrical shapes of objects in two-dimensional images.
ãã2. In order to reduce the statistical bias in the output of traditional morphological open-closing and clos-opening filters, this dissertation presents a new class of generalized open-closing (GOC) and clos-opening (GCO) morphological filters by using two different sized of structuring elements and proves that this class of filters possess the four fundamental properties (translation invariance, monotonically, duality and idempotence). In order to understand their filtering processes well, this dissertation analyzes the root signal characteristics of generalized morphological filters based on above method of signal state modeling. With the aid of positive Boolean function(PBF) descriptions, the generalized morphological filters are expressed as a kind of stack filters. The analytic expressions of output functions of GOC and GCO filters with one-dimensional convex structuring elements are derived form the statistical properties of stack filters. We analyze the statistical regularities of this kinds of filters and calculate the numerical features(means and variances). In addition, an adaptive weighted combination generalized morphological filter is proposed on the basis of GOC/GCO filters and adaptive processing method. The simulation verifications of one-dimensional and two-dimensional signals give satisfying results.
ãã3. On the basis of multitemplate-matching method, this dissertation introduces linear multiple structuring elements to GOC and GCO filters, and gives the definitions of a parallel-complex generalized morphological filter. Moreover, an adaptive weighted averaging generalized algorithm is investigated by using the constrained least-mean-squared(CLMS)error method. Simulation results have shown that filtering algorithm above is efficient.
ãã4. In this dissertation, we define a class of maximum-opening and minimum-closing operations based on the omnidirectional structuring elements, and further construct a class of omnidrectional multistages combination morphological filters by their difficult orders cascading. Finally, an omnidrectional multistages weighted combination morphological filtering algorithm is presented by means of weighted averaging operations of morphological transformations. The computer simulation results show that this algorithm has an excellent performance on noise-suppressing and geometrical features-preserving.
ãã5. The optimizing problems of ranked-order morphological filtering are investigated. We point out that structuring elements and percentiles have the influences on the filtering results. According to the limitation of the filters with fixed parameters, Under the mean-square-error (MSE) and mean-absolute-error (MAE) criteria, adaptive processing of percentiles and structuring elements in ranked-order morphological filtering are implemented by using the adaptive LMS algorithm in this dissertation. These filters have the important applications in the cases of the filtering to noisy step-variance signals.
ããThe results obtained in this dissertation have published more than 20 papers with academic values. Furthermore, many papers have been recorded by the authority international indexes and abstracts. They have the important academic meanings. This dissertation not only has made major progress in principle, but also has the important applications in the practical engineering projects. There are many economical benefits to be obtained remarkably.
ããThe achievements of the dissertation have the significant academic values to enrich the thesaurus of nonlinear digital signal processing and have the instructional meanings to develop the other nonlinear filters. Especially, they have the active influences on accelerating the subjects of image processing, computer vision and mode recognition. They have the wide applications in many fields such as aviation and space remote sensing, image mated guide, artificial intelligence, robot vision, biologic medicine, seism and sonar signal processing.
ããKey words: Mathematical morphology, morphological filters, structuring elements, nonlinear filtering, image processing
温馨提示:答案为网友推荐,仅供参考