ISWC OpenIR  > 水保所知识产出(1956---)
多分辨率分析方法在 DEM 多尺度表达中的应
王海江
Subtype博士
Thesis Advisor李 锐
2013-05
Degree Grantor中国科学院研究生院
Place of Conferral北京
Keyword多尺度表达 Dem 综合 分辨率 多分辨率分析 采样定理
Abstract

空间现象和规律只有在一定的尺度下才会出现,经过合理的尺度抽象的空间信息
更加具有利用价值。多尺度地理信息系统与单一尺度的地理信息系统相比更能满足用
户的需要。数字高程模型(Digital Elevation Model, DEM)作为地貌形态的重要表达
方式,是进行其它学科研究的重要支撑数据。基于 DEM 的应用已不再局限于常规的
地表形态表达,己经上升到基于多种地形指标的地表过程动态模拟、地学多尺度建模
等更高层次,需要尺度或分辨率能够连续变化的、空间定位一致性较好的 DEM 数据
作为支撑

。多分辨率分析(Multi-scale Resolution Analysis, MRA)方法为表达不同
分辨率的 DEM 提供了有效途径。多分辨率分析方法可自适应的调节信号的不同频率
成分在空间域采样的疏密度,能够合理的对空间信息的低频宏观特征与高频微观细节
进行分析处理,在刻画多源、多尺度、海量空间数据集的基本特征方面具有强大优势。
借助多分辨率分析思想建立尺度依赖的空间数据表达模型,实现对空间数据的多尺度
自动处理具有重要的理论意义与实践价值。国内外针对基于 MRA 的 DEM 多尺度
② 表
达已有若干方面研究,但仍有一些关键问题尚未解决。
首先,现有研究对基于 MRA 的 DEM 多尺度表达的基本原理、对该方法生成的
DEM 的分辨率未有实质性探讨。其次,现有的基于 MRA 的 DEM 连续尺度表达方法
缺乏严密系统的理论依据。此外,现有的基于 MRA 的 DEM 多尺度表达方法采用的
MRA 方法(单小波变换)在结构性能上存在缺陷;一些新的 MRA 方法(如多小波
变换、轮廓波变换)已在许多图像处理领域显现出优势,但尚未引入到空间信息尺度
变换领域。本研究围绕以上问题对 MRA 方法在 DEM 多尺度表达方面的应用进行了
探索。
(1) 探讨了基于 MRA 的 的 DEM  多尺度与连续尺度表达的基本原理。以地学理
论与信号处理原理为理论依据,阐述了 DEM 尺度、分辨率、采样间隔之间的联系,分析了 DEM 频域最高频率与空间域分辨率之间的制约关系;探讨了基于 MRA 的
DEM 多尺度(或连续尺度)表达方法通过逐级(或逐量)降低 DEM 频域最高频率
生成分辨率逐级变化(或连续变化)的 DEM 的基本原理。
(2) 阐述了现有的小波变换 DEM  多尺度表达(即基于小波变换的 DEM 多尺
度表达,其它类同)方法的基本原理;对现有小波变换多尺度表达方法采用的小波
的结构进行了拓展,构建了三族性能更为优越的高平衡阶多进制(即
多尺
度表达,其它类同)方法的基本原理;对现有小波变换多尺度表达方法采用的小波
的结构进行了拓展,构建了三族性能更为优越的高平衡阶多进制(即 M  进制, M>2 ,


且 M )多小波系统;对所构建的多小波系统与改进后的 DEM 多尺度表达方法的
优越性进行了实验论证。
多尺度表达方法的
优越性进行了实验论证。首先探讨了常用的小波变换(包括二进制与 M 进制小波变
换)的频域实现过程;阐述了小波变换通过对逐层低通滤波生成分辨率逐级降低的综
合 DEM 的实质;解释了由常见的小波变换 DEM 多尺度表达方法生成的 DEM 的分
辨率及其与分解层数之间的关系,确定了该方法生成的综合 DEM 的分辨率。然后借
鉴已有的高阶平衡二进制多小波的构建原理,依据通过构造、求解方程组来构建小波
滤波器组的思路,借助 Gröbner 基技术成功构造了三族多小波系统:三进制正交对称
二重小波,三进制正交翻转对称二重小波与四进制正交对称二重小波。各族多小波系
统均涵盖三级平衡阶,即包含一阶、二阶、三阶平衡多小波,且支集长度相对于各平
衡阶最短。最后将所构建的 M 进制多小波系统应用于 DEM 多尺度综合应用中,通过
实验论证了所构建的 M 进制多小波系统与 M 进制单小波系统、二进制多小波系统以
及二进制单小波系统相比在获得相同目标分辨率或综合程度的同时,能够有效的降低
综合误差。
(3) 构建以信号处理原理为理论依据的、有效的 DEM  连续尺度变换方法。探
讨以采样定理为依据的、通过合理划分频带与处理频带定量限制 DEM 频域最高频率
生成指定分辨率 DEM 的 DEM 连续尺度变换原理;改进频带划分需要借助的分数进
制小波变换,使其各分解层带通滤波器的品质因子(Q-factor)均可按需调控,实现
频域自由分割,同时通过张量积变换将一维分数进制小波变换拓展,获得其二维形式,
为 DEM 连续尺度表达提供方法支持;验证所构建的基于采样定理与分数进制小波变
换的 DEM 连续尺度表达方法的有效性(包括分辨率的有效性,空间定位的一致性以
及综合效果的合理性等方面)。
(4) 构建分数进制轮廓波变换,改进分数进制小波变换 DEM 连续尺度表达方
法,提高方法对
连续尺度表达方
法,提高方法对 DEM  局部地形、轮廓边缘保持能力。将分数进制小波变换中的尺度
变换与轮廓波变换中的多方向变换整合,同时通过合理设置尺度变换滤波器的截止频
率消除原轮廓波变换中存在的频域混叠成分,最终获得具备抗混叠性质的、频域分割
更为自由精细的、多方向性的分数进制轮廓波变换。通过图像处理实验验证该方法在
图像处理领域的优势。借鉴分数进制小波变换 DEM 连续尺度变换原理,将该变换方
法应用于 DEM 综合领域,论证了该方法的有效性与适用性。(5) 通过实验对本文所构建的三种基于 MRA 的 的 DEM  尺度变换方法(M 进制
多小波变换
进制
多小波变换 DEM  多尺度表达、分数进制小波变换 DEM 连续尺度表达、分数进制轮
廓波变换
连续尺度表达、分数进制轮
廓波变换 DEM 连续尺度表达)以及常规插值变换方法(双线性、双三次插值方法)
进行了综合比较,探讨了各方法的优缺点与适用环境。
连续尺度表达)以及常规插值变换方法(双线性、双三次插值方法)
进行了综合比较,探讨了各方法的优缺点与适用环境。实验数据选用了具有不同地形
起伏特征的 DEM 与具有可对比真值的由数学连续曲面生成的 DEM。结果表明,M
进制多小波变换 DEM 多尺度综合与常规插值方法相比,能够有效降低综合误差;同
时算法简捷高效,执行耗时少,硬件配置要求较低,可深入推广到 DEM 多尺度表达
领域。然而由该方法生成的 DEM 序列的分辨率为间断序列,无法实现连续尺度变换。
分数进制小波变换 DEM 综合可以实现 DEM 的连续尺度变换;目标分辨率相同时,
综合误差与 M 进制多小波变换 DEM 综合方法相比相近;与后者相比,虽算法稍复杂,
执行耗时稍长,但仍能被大多数运行环境所接受。所有方法中,分数进制轮廓波变换
DEM 综合算法生成的综合误差最小;能够更有效的保持 DEM 轮廓边缘的完整性与
连贯性,同时更好的抑制由综合过程产生的“虚假”地形现象。然而,与其它方法相
比,其算法最复杂,运行耗时较长,因此较适用于硬件配置较好的应用场景。
(6)依据基于采样定理与分数进制小波变换的 DEM 连续尺度表达方法的基本
原理,基于 MATLAB 软件提供的图形用户接口与编译平台,设计构建高精度、高效
率的 DEM 连续尺度变换应用程序。
关键词:多尺度表达,DEM 综合,分辨率,多分辨率分析,采样定理

Other Abstract

Spatial events and patterns only takes place in a certain scale, so the spatial
information after scientifically scale-abstraction is more valuable in practices. Multi-scale
geographical information system (GIS) is more useful for users than single-scale GIS.
Digital elevation model (DEM), as a significant approach to represent topography, is a
fundamental support dataset of the research of other areas. The applications of DEM are no
longer confined to the traditionally surface topographic representation and have expanded
to some higher levels, such as surface-process dynamically simulation and multi-scale
geographical modeling. These applications need the DEM database which can provide
representation of terrain with continuously-changing scale (or resolution) and consistent
spatial location base well. The idea of multi-scale resolution analysis (MRA) introduces an
effective way to represent and analyze the spatial information (e.g., DEM) with different
resolution. The MRA can adaptively control the sampling rate of different frequency
components of signals in spatial domain. For spatial information, this methodology can
reasonably analyze and process their low-frequency macro-scale characteristics and
high-frequency micro-scale details as well. This methodology thus shows desirable
advantages in representing the fundamental characteristics of the spatial information
database of multi-sources, multi-scale and mass-quantity. It is of great value in theory and
practice to use MRA methods to establish the scale-depended spatial information
representation model and to employ the multi-scale and automatic processing to spatial
information dataset. Researchers have carried out studies in several ways. However, some
key problems are still left behind.
Firstly, the present studies have not analyzed and revealed the fundamental principle
of the MRA based DEM multi-scale representation and the resolution obtained. Secondly,  the MRA methods used by the existing MRA based DEM multi-scale representation have
some drawbacks. Some improved MRA methods (e.g., Contourlet, Multiwavelet) have
been shown some significant advantages in many image processing fields, but haven’t been
introduced into the application field of spatial information scale-transformation. This work
focuses on the above issues and studies the application of MRA to DEM multi-scale
representation in the following aspects.
(1) The fundamental principle of the MRA based DEM multi-scale
representation is analyzed. According to the geophysical theory and signal processing
principle, this study describes the relationship among the scale, resolution and sampling
interval of DEM and analyzes the constraint relation between the highest frequency (in
frequency domain) of DEM and their resolution (in spatial domain). Furthermore, the work
reveals the fundamental principle of the MRA based DEM multi-scale representation,
which  generates  DEM  with  levelly/continuously  coarsening  resolution  by
levelly/continuously lessening the highest frequency of DEM.
(2) This study reveals the fundamental principle of the traditional wavelet
transform (WT) based DEM multi-scale representation methods, improves the
structure of the WT used by the present WT based multi-scale representation
methods, constructs three families of high-order balanced M-band ( M>2 and
M ) multiwavelet system which is more desirable than the WT in structure, and
finally verify their advantages via practical application in DEM multi-scale
generalization. Firstly, we study the frequency-domain behavior of the traditional WT
(including 2-band and M-band), describe the whole process of the WT based DEM
generalization which generates DEM with levelly-coarsening resolution by levelly-filtering
(of low-pass) in frequency domain, explain the relationship between the resolution of
generalized DEM and decomposition levels of WT when using traditional WT based
generalization method, and clarify the resolution obtained by the methods. We then study
the existing construction theory of high-order balanced 2-band multiwavelet that constructs
the WT filter bank by solving polynomial equation systems with the help of Gröbner-base
technique. Inspired by this idea, we successfully construct three families of M-band
multiwavelet, including three-band symmetric family, three-band flipped family and
four-band symmetric family. Each family is with the multiplicity of two, indexed by an
increasingly balanced order   ( {1,2,3}   , i.e. the balanced order of the multiwavelets in
each family ranges from one to three), and supported with the minimal length according to
every balanced order. The coefficients of the filter bank of each wavelet system are obtained. Finally, we apply these constructed multiwavelet systems to the application of
DEM generalization. The results show when providing same generalization scale or
resolution, they can effectively reduce the generalized errors compared with 2-band
multiwavelets, M-band scalar wavelets and 2-band wavelets. Also, the effectiveness of
high-order balanced property in these multiwavelet systems are tested and verified.
(3) The study proposes a scale-continuously-changing transform of DEM which
is effective and signal-processing theory based. We study the principle of the proposed
transform that is based on sampling theory and generates DEM with assigned resolution by
quantitatively lessening the highest frequency of DEM. Then, we improve a kind of
rational-dilation wavelet transform (RWT) to meet the requirement of the proposed
transform, i.e., to make the Q-factor at each decomposition level tunable to realize freely
frequency-domain partition and to expand the one-dimensional RWT to its
two-dimensional counterpart by using tensor product operation. We also evaluate the
performance of the scale-continuously-changing transform in DEM generalization
application, and the experimental results show its effectiveness (including the satisfactory
of generalized results with the sampling theory, the desirable-consistency spatial location
base, and effectiveness of the generalization). 
(4) We propose a new effective image representation approach (Tunable-Q
Contourlet Transform) to improve the RWT based scale-continuously-changing
transform of DEM, and to improve the ability in retaining the local terrain and
contours. We integrate the multi-scale transform scheme of the rational-dilation wavelet
transforms and the directional filter bank of original contourlets, and eliminate the
frequency-domain aliasing component in the contourlets by reasonably employing the
stop-edge frequency of the filter bank of the multi-scale transform. We consequently obtain
the anti-aliasing tunable-Q contourlet transform which provides finer frequency-domain
partition and more sensitive directional information representation. Experiments are
implemented to evaluate its performance in image processing and the results show its
advantages in image approximation and de-noising. By using the scale (or resolution)
continuously-changing generalization principle of the proposed rational-dilation wavelet
transform based DEM representation, we apply the tunable-Q contourlet transform to DEM
generalization field and our results show its applicability and advantages.
(5) We take a comparative analysis to different DEM multi-scale representation
methods, including the three proposed methods (the M-band multiwavelet transform
based method, the rational-dilation wavelet transform based method and the
tunable-Q contourlet based method) and the traditional interpolation approaches  (bilinear and bicubic), in order to evaluate their practical performance and
applicability environment. The datasets used in the experiments include the DEM
datasets with different terrain characteristics and the DEM derived from ideal mathematic
surface which provides reference real value in comparison. The experimental results show
the DEM multi-scale transform based on the proposed M-band multiwavelet transform can
effectively reduce the generalization error compared with traditional interpolation methods.
Meanwhile, its algorithm is comparatively simple and the execution is efficient, so it only
requires low-level equipment and is suitable for most of application environments.
However, the resolution cases provided by its generalized results is some discreet array,
this mean the methods can not realize a scale continuously-changing representation. The
rational-dilation wavelet transform based DEM generalization method does this well and
its generalized results provide us with continuously-changing resolution. The method
results in same generalization precision compared with the M-band multiwavelet based
method, for same goal resolutions. Additionally, it has moderate-level computation
complexity and execution time, and is suitable for general users. For all the test methods,
the tunable-Q contourlet based method obtains the highest generalized precision. It not
only better retains the integrity and continuity of the contours or edges of DEM, but also
more effectively reduces the ‘artificial’ terrain features. On the other side, it incurs a more
complicate computational complexity and requires more computational time. So this
method is suitable for application environment with high-level execution equipment.
(6) According the main idea of the proposed DEM representation based on
rational-dilation wavelet transform and sampling theory, we design application program for
scale continuously-changing generalization of DEM. The program is established in
MATLAB software and supported by its Graphical User Interface (GUI) and its
interpreting and publishing packages. Our program provides a friendly interactive interface
and stable and effective execution process.
Key words: Multi-scale representation; DEM generalization; Multi-resolution analysis;
Sampling theory 

Language中文
Document Type学位论文
Identifierhttp://ir.iswc.ac.cn/handle/361005/8969
Collection水保所知识产出(1956---)
Recommended Citation
GB/T 7714
王海江. 多分辨率分析方法在 DEM 多尺度表达中的应[D]. 北京. 中国科学院研究生院,2013.
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