## Compressing Digital Elevation Models with Wavelet Decomposition (2001)

Citations: | 2 - 0 self |

### BibTeX

@MISC{Ottoson01compressingdigital,

author = {Patrik Ottoson},

title = {Compressing Digital Elevation Models with Wavelet Decomposition},

year = {2001}

}

### OpenURL

### Abstract

Wavelet decomposition is a well-known technique to compress image data. Here, we have used wavelet decomposition to compress digital elevation models, DEM. The objectives for compressing DEMs are obtaining manageable and small data sets, and reducing data access time. In the paper, different aspects of wavelets as a base for data compression are described. The (de-)compression scheme consists of three steps: wavelet decomposition, quantization, and de-/encoding. A few selected techniques to carry out these steps are presented here. Wavelet decomposition does not destruct or compress data. In the decomposition, data are re-organised in a way that facilitates compression. In the quantization step, data can be destructed. It is shown that the quantizer can be constructed to obtain high compression ratios and a low degree of destruction of data. An adaptive quantizer that considers the distribution of data gives the best result. Performance measures for the 50x50 m DEM of all of Sweden are presented.

### Citations

2062 |
Handbook of mathematical functions
- Abramovitz, Stegun
- 1972
(Show Context)
Citation Context ... number of levels, x 2 ,..., xL are the decision levels and y 1 ,..., y L are the representation levels. p ( x) is a probability density function (PDF), in our case the Gaussian (normal) distribution =-=[1] p ( x) =-=- 1 x e 2π The decision and representation levels are computed from the following expressions 1 x k = k −1 + 2 2 − k / 2 ( y y ) xk + 1 ∫ xk xk + 1 ∫ k ( x) y = . k xk xp p ( x) dx dx . and x(... |

1585 | Orthonormal bases of compactly supported wavelets
- Daubechies
- 1988
(Show Context)
Citation Context ...), which means that the bandwidth is halved [13]. The relation between H and G is 1−n ( −1) h n g n = 1− where n is the coefficient's number. A well-known mother wavelet is the Daubechies' W6-wa=-=velet [2]-=-. The W6transformed coefficients will be zero for any signal that can be approximated by a polynomial of degree two or less. This property fits well with elevation data, because we believe that elevat... |

1251 |
Embedded image coding using zerotrees of wavelet coefficients
- Shapiro
- 1993
(Show Context)
Citation Context ...ly, codecs compress data without loss of information. There exists many codecs, which are optimised for speed, compression ratio or quality. For best possible quality, the Shapiro's Zero Tree encoder =-=[12]-=- should be used, but the compression time is very long. We decided to use a simple run-length encoder (RLE), which should give acceptable results. Because of its simplicity, the RLE codec can be const... |

206 |
Quantizing for minimum distortion
- Max
(Show Context)
Citation Context ...7). We construct an adaptive quantizer as a uniform quantizer, but the step lengths are adapted to the distribution of data. These step lengths can be determined experimentally. A Lloyd-Max quantizer =-=[8] is a -=-quantizer, which minimises the mean-square quantization error. The length of the steps for the Lloyd-Max quantizer is determined by minimising the quantization variance 2 q L x k + 1 ∑ ∫ 2 ( x −... |

197 |
Zur Theorie der orthogonalen Funktion Systeme
- Haar
- 1910
(Show Context)
Citation Context ...unctions or operators into different frequency components [3]. The wavelet f x as a set of wavelets or basis functions, transform can represent a function ( ) f n ∑ i= 0 ( x) = c ψ ( x) i i 2 (2) (=-=3) (4) -=-(5)sψ are basis functions, c i are coefficients or weights and n is the number f has to be a signal (a set) of correlated values. For example, adjacent elevation points or image pixels are correlated... |

167 |
Subband Coding of Images
- Woods, O’neil
- 1986
(Show Context)
Citation Context ...velet transforms can be seen as a form of sub-band filters or quadrature mirror filters (QMF). A signal is filtered by a low-pass (H) and highpass filter (G), which means that the bandwidth is halved =-=[13]. The -=-relation between H and G is 1−n ( −1) h n g n = 1− where n is the coefficient's number. A well-known mother wavelet is the Daubechies' W6-wavelet [2]. The W6transformed coefficients will be zero... |

117 | An overview of wavelet based multiresolution analysis
- Jawerth, Sweldens
- 1992
(Show Context)
Citation Context ...levels x k Inverse yk yk Normalise data Quantize quantization Re-normalise data x − μ x x′ = σ x Fig. 9. Flowchart of the quantization and coding process (a modified version from Jawerth and Swe=-=ldens [5]-=-). y k x x y ks2.5 Coding Software that encodes and decodes data is often called a codec. Normally, codecs compress data without loss of information. There exists many codecs, which are optimised for ... |

98 |
lectures on wavelets, volume 61
- Ten
- 1992
(Show Context)
Citation Context ...tions used to identify a given function in space (translation) and scale (contraction). The wavelet transform is a tool that separates data, functions or operators into different frequency components =-=[3]. Th-=-e wavelet f x as a set of wavelets or basis functions, transform can represent a function ( ) f n ∑ i= 0 ( x) = c ψ ( x) i i 2 (2) (3) (4) (5)sψ are basis functions, c i are coefficients or weight... |

26 |
Experiments in picture representation using regular decomposition, Computer Graphics Image Processing 5
- Klinger, Dyer
- 1916
(Show Context)
Citation Context ... which lead to large amounts of data. DEMs are usually stored as grids, TIN models or adaptive quadtrees (fig. 1). Fig. 1. A regular grid, an irregular triangular network (TIN), and an quadtree model =-=[6]-=-.sGeographic data sets are often large: describing Sweden using a 50x50 m 2 grid database of elevations and land use classification including pointers to denser data for selected areas, requires appro... |

4 |
Digital image processing, Wiley-Interscience Publication, 2 nd Edition
- Pratt
- 1991
(Show Context)
Citation Context ...n data with decimetre resolution, 16 bits can represent elevations between -3276.8 and +3276.7 m, which is sufficient for Sweden. 2. The minimal number of bits required to code data is called entropy =-=[11], wh-=-ich given in bits per pixel (bpp) is expressed as H = − T ∑ i= 1 p log p . i pi is the probability of occurrence of an elevation value and T is the numbers of nonzero occurrences. This is called t... |

2 |
Quadtree Surface Representation and Artificial Textures in Landscape Visualisation
- Ottoson
- 2002
(Show Context)
Citation Context ...tain data quality. The elevation model used in the tests is reported to have an overall RMSE of 2-3 metres. This RMSE varies depending on terrain - lower for flat terrain and higher for hilly terrain =-=[9]-=-. The accuracy of the compression should be kept inside this limit. Tables 1-3 show that the adaptive quantizer gives the best result regardless of decomposition of wavelet transform used. Fig. 16 sho... |

2 |
Virtual Reality in Visualisation, Planning and Design of Roads
- Ottoson
- 1999
(Show Context)
Citation Context ...ften large: describing Sweden using a 50x50 m 2 grid database of elevations and land use classification including pointers to denser data for selected areas, requires approximately 9 Gbyte of storage =-=[10]-=-. A resent trend is to produce orthophotos over cities and other areas of interest. The construction of an orthophoto requires access to a DEM with a resolution 10-50 times coarser than that of the or... |