小波与细分方法在图像处理中的应用研究
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摘要
小波分析于80年代末取得了突破成就,Daubechies提出了构造具有紧支撑的正交小波,Mallat提出的多分辨和快速离散小波变换。小波已经涉及或应用到信息领域的所有学科,是目前国际上最新的时频分析工具。小波应用的巨大成功提升了人们继续探索其新理论和新方法的热情,其中最为突出的是90年代中期提出的提升方法,它是构造小波和实现小波变换的一种新方法。提升方法已经被国际标准组织ISO所采纳,并由此导致了第二代小波的诞生,其中细分小波便是第二代小波的典型代表。本文着重讨论基于小波和细分方法在图像处理技术中的应用研究。
基于小波变换的图像去噪是图像去噪的主要方法之一,本文总结了基于单小波图像去噪的基本方法和每种方法的优缺点。本文利用小波系数的相关性和信号与噪声的小波系数模极大值在不同尺度间具有不同的传播特性,提出了基于小波尺度乘积与阈值相结合的图像去噪算法。实验表明,该算法在信号去噪方面具有较好的去噪效果。
细分方法是近年来计算机辅助几何设计和计算机图形领域中研究的一个热点问题,本文首先回顾了细分方法的发展概况,然后介绍了细分方法的基本理论、特点、分类和应用。本文通过对细分和细分小波的研究,提出了一种新的四点插值细分小波,并利用细分方法具有的多分辨率分析特性,将细分方法应用到图像处理中。对细分方法在图像中的应用进行了初步探索和研究,主要体现在图像分割、图像匹配和图像修复等方面。
图像分割是图像分析和计算机视觉中非常重要的研究内容,它根据图像中一个或多个特征将图像分成某些感兴趣的区域,是图像分析、理解的关键,也是图像处理的经典难题之一。图像分割的应用非常广泛,几乎出现在有关图像处理的所有领域,并涉及各种类型的图像。本文通过对图像分割方法的比较研究,对目前常用的图像分割算法进行了总结和评述。近年来,Mean-Shift聚类算法受到了广泛的关注,它是一种核密度估计的非监督聚类方法,在图像分割中具有良好性能,但不足的是该算法计算量比较大,运行时间较长。本文利用提出的四点插值细分小波,给出了基于细分小波与Mean-Shift聚类算法相结合的图像分割算法,该算法在基本保持Mean-Shift算法的分割性能的前提下,显著地提高了图像的分割速度。
数字图像匹配技术是模式识别和图像处理的基本手段,它已在卫星遥感、空间飞行器的自动导航、机器人视觉、气像云图分析及医学X射线图片处理等许多领域得到了广泛的应用。图像匹配技术所要解决的主要问题是:在保证一定匹配精度的前提下,如何进一步提高图像的匹配速度。传统的模板匹配法概念清晰,实现简单,但计算量十分庞大,不能满足图像处理的实时性要求。针对上述问题,本文利用立方B样条细分小波,提出了基于细分小波的局部投影熵的图像匹配算法,该算法在一定程度上解决了匹配速度问题。并将该算法应用到自主移动机器人跟踪问题中,得到了较好的结果。
图像破损以及数据丢失是图像经压缩、传输、解压缩过程中经常遇到的问题,这一问题在图形图像处理领域中已经引广泛关注,图像破损中较为严重的情况是像素群丢失,如图像经编码后在传输中受到干扰而出现解码后的像素群丢失,或由解码技术本身决定的图像不能完全复原。针对单像素丢失,常见的解决方法为简单的邻点平均法和中指滤波法。对像素群丢失的情况则问题比较复杂,只能根据待修复区域适当范围内的像素所含信息通过建立的修复规则进行修复,要想完全修复是不可能的。本文利用细分方法在几何造型方面的优势,提出了基于四点插值细分的图像修复算法,该方法来源于计算机辅助几何设计研究领域中三维空间自由曲线曲面造型技术。使用该方法不仅可以修复不规则像素群,而且修复边缘具有很好的平滑过渡性。
细分方法以其简单的表示、不同层间良好的逼近性质被广泛地应用于自由曲线曲面造型设计中。将细分方法引入到主曲线设计的光滑拟合中,收到了很好的效果。首先分别采用邻域法、投影法对散乱数据进行初始化以获取初始控制多边形顶点;然后对初始控制多边形进行细分从而产生光滑主曲线。该文还对邻域-细分法和投影-细分法获得的主曲线特点进行了比较分析,这为从需求出发选择主曲线设计方法提供了参考依据。该主曲线设计方法具有表达简洁,计算量小、自相合性等优点。
In the late 1980s,Daubechies proposed a systematical approach of constructing compactly supported orthogonal wavelet and Mallat presented multiresolution analysis and fast discrete wavelet transform. Wavelet analysis have been applied to or involved in all fields of information domain and is internationally recognized as the most new tool of time-frequency analysis. The successful application of wavelet made people full of passion to explore the new theories and methods. Lifting wavelet was proposed in the middle of the 1990's. It is one of the best methods and a new method of realizing wavelet construction and transform. Lifting scheme had been adopted by ISO and it caused the birth of the Second Wavelet. Subdivision wavelet is the classical representation of the second generation wavelet. This paper takes importance of the applied research in the image processing based on wavelet and subdivision scheme.
Because image denoising based on wavelet transform is an important method in image denoising,the paper summaries the basic image denoising methods based on single wavelet and each method's advantages and defects.This paper makes use of the relation of the wavelet coefficients and the different spreading characteristics of wavelet coefficients modular maximum between signal and noise in the different scales. Then the image denoising algorithm based on combining multi-scale product with wavelet threshold shrinkage is proposed in this paper. The experiments demonstrate that the algorithm proposed in the paper possesses preferable effect in image denoising.
Subdivision scheme has become a focus of study in the world in computer aided geometric design and computer graphics recent years. After reviewing the general situation and history of subdivision, we introduce the elementary theories, the characteristic, the classification and application of subdivision. Through studying subdivision and subdivision wavelet, a new 4-point interpoloary subdivision wavelet is proposed in this paper. Then it is applied in image processing due to its muiltresolution analysis feature. The paper gave a primary discussion and research about the applications of subdivision scheme in image processing, which include image's segmentation, matching and repairing.
Image segmentation is an important research content in image analysis and computer vision. It's task is segmenting the image into some areas according to one or lots of features of image. It is the key of image analysis and understanding and also the classic problem in image processing. Image segmentation is widely used in almost all fields of image processing. It involves all kinds of images. This paper summarizes and appraises usual algorithms of image segmentation through comparative study among different segmentation methods.Mean-Shift clustering algorithm is widely paid attention recently years. It is a nuclear density estimation and non-supervision clustering method. It possesses favorable capability in image segmentation. It's defects are excessive computational cost and long running time. An image segmentation algorithm is presented combining 4-point interpoloary subdivision wavelet proposed in this paper with Mean-Shift clustering method. It promotes the speed of image segmentation in the condition of keeping Mean-Shift algorithm's segmentation effect.
Digital image match is the basic method in pattern recognition and image processing. It is widely used in satellitic remote sensing, automatic airmanship of space aerocraft, robot vision, meteorologic nephogram analysis and X-radial image processing in medicine. The primary problem to resolve in image match is promoting the speed in keeping some precision of image match. Classical template match algorithms have clear concept and it is simple to implement. But it has expensive computational cost so that it cann't satisfied real-time demand in image processing.According to the above questions, the image match algorithm based on local projection entropy and cubic B-spline subdivision wavelet was proposed in this paper. It promotes the speed of image match in some extent.This algorithm is applied to the tracking object of autonomous mobile robot and obtained good result.
Image corruption and loss of data are always encountered in the processing of image compression, transmision and decompression, which had been paid attention by many researcheres who working on image processing. The loss of pixel groups when image encoding or incomplete restoration determined by decompression technique itself. For single pixel loss, general solution is to adopt the neighborhood point mean method and medium filter. When loss of pixel groups, the restoration is more difficult and sometimes it is impossible to restore the damaged image completely. Whereas, the relative information of appropriate fields around the pixel groups is chosen and some reasonable rule is established to restore the image .But complete restoration of the image is impossible. Using the advantage of subdivision in geometry modeling, the image repair algorithm based on 4-point interpoloary is presented in the paper. The subdivision come from modeling techniques of three dimensional free curve and surface in the domain of computer aided geometric design. Not only the groups of non-regular pixels can be repaired but also the repairing edges possess better smooth transition effect.
Subdivision method has been widely applied to free curves and surfaces design for its simple representation and good approximating property among different layers. In the paper, subdivision has been introduced to the design of smooth principal curve and the good result has been obtained. First of all, in order to gain vertices of the initial control polygon the scattered data were initialized by Circle or Projection method. Then subdivide the initial control polygon some times and generate smooth principal curve. The comparison has been implemented between the principal curves generated from Circle-subdivision and Projection-subdivision apart. This offers reference for choosing the principal curve design method according to the target. The principal curve design method has the properties of simple representation, low cost and self-consistency.
基于小波变换的图像去噪是图像去噪的主要方法之一,本文总结了基于单小波图像去噪的基本方法和每种方法的优缺点。本文利用小波系数的相关性和信号与噪声的小波系数模极大值在不同尺度间具有不同的传播特性,提出了基于小波尺度乘积与阈值相结合的图像去噪算法。实验表明,该算法在信号去噪方面具有较好的去噪效果。
细分方法是近年来计算机辅助几何设计和计算机图形领域中研究的一个热点问题,本文首先回顾了细分方法的发展概况,然后介绍了细分方法的基本理论、特点、分类和应用。本文通过对细分和细分小波的研究,提出了一种新的四点插值细分小波,并利用细分方法具有的多分辨率分析特性,将细分方法应用到图像处理中。对细分方法在图像中的应用进行了初步探索和研究,主要体现在图像分割、图像匹配和图像修复等方面。
图像分割是图像分析和计算机视觉中非常重要的研究内容,它根据图像中一个或多个特征将图像分成某些感兴趣的区域,是图像分析、理解的关键,也是图像处理的经典难题之一。图像分割的应用非常广泛,几乎出现在有关图像处理的所有领域,并涉及各种类型的图像。本文通过对图像分割方法的比较研究,对目前常用的图像分割算法进行了总结和评述。近年来,Mean-Shift聚类算法受到了广泛的关注,它是一种核密度估计的非监督聚类方法,在图像分割中具有良好性能,但不足的是该算法计算量比较大,运行时间较长。本文利用提出的四点插值细分小波,给出了基于细分小波与Mean-Shift聚类算法相结合的图像分割算法,该算法在基本保持Mean-Shift算法的分割性能的前提下,显著地提高了图像的分割速度。
数字图像匹配技术是模式识别和图像处理的基本手段,它已在卫星遥感、空间飞行器的自动导航、机器人视觉、气像云图分析及医学X射线图片处理等许多领域得到了广泛的应用。图像匹配技术所要解决的主要问题是:在保证一定匹配精度的前提下,如何进一步提高图像的匹配速度。传统的模板匹配法概念清晰,实现简单,但计算量十分庞大,不能满足图像处理的实时性要求。针对上述问题,本文利用立方B样条细分小波,提出了基于细分小波的局部投影熵的图像匹配算法,该算法在一定程度上解决了匹配速度问题。并将该算法应用到自主移动机器人跟踪问题中,得到了较好的结果。
图像破损以及数据丢失是图像经压缩、传输、解压缩过程中经常遇到的问题,这一问题在图形图像处理领域中已经引广泛关注,图像破损中较为严重的情况是像素群丢失,如图像经编码后在传输中受到干扰而出现解码后的像素群丢失,或由解码技术本身决定的图像不能完全复原。针对单像素丢失,常见的解决方法为简单的邻点平均法和中指滤波法。对像素群丢失的情况则问题比较复杂,只能根据待修复区域适当范围内的像素所含信息通过建立的修复规则进行修复,要想完全修复是不可能的。本文利用细分方法在几何造型方面的优势,提出了基于四点插值细分的图像修复算法,该方法来源于计算机辅助几何设计研究领域中三维空间自由曲线曲面造型技术。使用该方法不仅可以修复不规则像素群,而且修复边缘具有很好的平滑过渡性。
细分方法以其简单的表示、不同层间良好的逼近性质被广泛地应用于自由曲线曲面造型设计中。将细分方法引入到主曲线设计的光滑拟合中,收到了很好的效果。首先分别采用邻域法、投影法对散乱数据进行初始化以获取初始控制多边形顶点;然后对初始控制多边形进行细分从而产生光滑主曲线。该文还对邻域-细分法和投影-细分法获得的主曲线特点进行了比较分析,这为从需求出发选择主曲线设计方法提供了参考依据。该主曲线设计方法具有表达简洁,计算量小、自相合性等优点。
In the late 1980s,Daubechies proposed a systematical approach of constructing compactly supported orthogonal wavelet and Mallat presented multiresolution analysis and fast discrete wavelet transform. Wavelet analysis have been applied to or involved in all fields of information domain and is internationally recognized as the most new tool of time-frequency analysis. The successful application of wavelet made people full of passion to explore the new theories and methods. Lifting wavelet was proposed in the middle of the 1990's. It is one of the best methods and a new method of realizing wavelet construction and transform. Lifting scheme had been adopted by ISO and it caused the birth of the Second Wavelet. Subdivision wavelet is the classical representation of the second generation wavelet. This paper takes importance of the applied research in the image processing based on wavelet and subdivision scheme.
Because image denoising based on wavelet transform is an important method in image denoising,the paper summaries the basic image denoising methods based on single wavelet and each method's advantages and defects.This paper makes use of the relation of the wavelet coefficients and the different spreading characteristics of wavelet coefficients modular maximum between signal and noise in the different scales. Then the image denoising algorithm based on combining multi-scale product with wavelet threshold shrinkage is proposed in this paper. The experiments demonstrate that the algorithm proposed in the paper possesses preferable effect in image denoising.
Subdivision scheme has become a focus of study in the world in computer aided geometric design and computer graphics recent years. After reviewing the general situation and history of subdivision, we introduce the elementary theories, the characteristic, the classification and application of subdivision. Through studying subdivision and subdivision wavelet, a new 4-point interpoloary subdivision wavelet is proposed in this paper. Then it is applied in image processing due to its muiltresolution analysis feature. The paper gave a primary discussion and research about the applications of subdivision scheme in image processing, which include image's segmentation, matching and repairing.
Image segmentation is an important research content in image analysis and computer vision. It's task is segmenting the image into some areas according to one or lots of features of image. It is the key of image analysis and understanding and also the classic problem in image processing. Image segmentation is widely used in almost all fields of image processing. It involves all kinds of images. This paper summarizes and appraises usual algorithms of image segmentation through comparative study among different segmentation methods.Mean-Shift clustering algorithm is widely paid attention recently years. It is a nuclear density estimation and non-supervision clustering method. It possesses favorable capability in image segmentation. It's defects are excessive computational cost and long running time. An image segmentation algorithm is presented combining 4-point interpoloary subdivision wavelet proposed in this paper with Mean-Shift clustering method. It promotes the speed of image segmentation in the condition of keeping Mean-Shift algorithm's segmentation effect.
Digital image match is the basic method in pattern recognition and image processing. It is widely used in satellitic remote sensing, automatic airmanship of space aerocraft, robot vision, meteorologic nephogram analysis and X-radial image processing in medicine. The primary problem to resolve in image match is promoting the speed in keeping some precision of image match. Classical template match algorithms have clear concept and it is simple to implement. But it has expensive computational cost so that it cann't satisfied real-time demand in image processing.According to the above questions, the image match algorithm based on local projection entropy and cubic B-spline subdivision wavelet was proposed in this paper. It promotes the speed of image match in some extent.This algorithm is applied to the tracking object of autonomous mobile robot and obtained good result.
Image corruption and loss of data are always encountered in the processing of image compression, transmision and decompression, which had been paid attention by many researcheres who working on image processing. The loss of pixel groups when image encoding or incomplete restoration determined by decompression technique itself. For single pixel loss, general solution is to adopt the neighborhood point mean method and medium filter. When loss of pixel groups, the restoration is more difficult and sometimes it is impossible to restore the damaged image completely. Whereas, the relative information of appropriate fields around the pixel groups is chosen and some reasonable rule is established to restore the image .But complete restoration of the image is impossible. Using the advantage of subdivision in geometry modeling, the image repair algorithm based on 4-point interpoloary is presented in the paper. The subdivision come from modeling techniques of three dimensional free curve and surface in the domain of computer aided geometric design. Not only the groups of non-regular pixels can be repaired but also the repairing edges possess better smooth transition effect.
Subdivision method has been widely applied to free curves and surfaces design for its simple representation and good approximating property among different layers. In the paper, subdivision has been introduced to the design of smooth principal curve and the good result has been obtained. First of all, in order to gain vertices of the initial control polygon the scattered data were initialized by Circle or Projection method. Then subdivide the initial control polygon some times and generate smooth principal curve. The comparison has been implemented between the principal curves generated from Circle-subdivision and Projection-subdivision apart. This offers reference for choosing the principal curve design method according to the target. The principal curve design method has the properties of simple representation, low cost and self-consistency.
引文
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