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Terrain data compression using wavelet-tiled pyramids for online 3D terrain visualization a
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Ricardo Olanda , Mariano Pérez , Juan Manuel Orduña & Silvia a
Rueda a
Departamento de Informática, University of Valencia, Valencia, Spain Published online: 01 Nov 2013.
To cite this article: Ricardo Olanda, Mariano Pérez, Juan Manuel Orduña & Silvia Rueda , International Journal of Geographical Information Science (2013): Terrain data compression using wavelet-tiled pyramids for online 3D terrain visualization, International Journal of Geographical Information Science, DOI: 10.1080/13658816.2013.829920 To link to this article: http://dx.doi.org/10.1080/13658816.2013.829920
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International Journal of Geographical Information Science, 2013 http://dx.doi.org/10.1080/13658816.2013.829920
Terrain data compression using wavelet-tiled pyramids for online 3D terrain visualization Downloaded by [University of Valencia], [Ricardo Olanda] at 07:10 04 November 2013
Ricardo Olanda*, Mariano Pérez, Juan Manuel Orduña and Silvia Rueda Departamento de Informática, University of Valencia, Valencia, Spain (Received 4 June 2013; final version received 22 July 2013) Last years have witnessed the widespread use of online terrain visualization applications. However, the significant improvements achieved in sensing technologies have allowed an increasing size of the terrain databases. These increasing sizes represent a serious drawback when terrain data must be transmitted and rendered at interactive rates. In this paper, we propose a novel wavelet-tiled pyramid for compressing terrain data that replaces the traditional multiresolution pyramid usually used in wavelet compression schemes. The new wavelet-tiled pyramid modifies the wavelet analysis and synthesis processes, allowing an efficient transmission and reconstruction of terrain data in those applications based on multiresolution tiled pyramids. A comparative performance evaluation with the currently existing techniques shows that the proposed scheme obtains a better compression ratio of the terrain data, reducing the storage space and transmission bandwidth required, and achieving a better visual quality of the virtual terrain reconstructed after data decompression. Keywords: virtual reality; terrain data compression; interactive terrain visualization; JPEG2000
1. Introduction Nowadays, online terrain visualization has become an essential part of many 3D online games (like Microsoft Flight Simulator (Microsoft 2013)), cartography applications (like Arc GIS (ESRI 2013)), earth visualization systems (like Google Earth (Google 2013)), or navigation systems (like GPS navigation applications). Remote sensing technologies have allowed a huge increase of both the size and resolution of digital elevation models (DEMs), as well as the corresponding photo textures. As a result, terrain visualization systems should deal with data sets that vastly exceed the available computing and/or graphical power, and network bandwidth. In recent years, many algorithms and methods, with different trade-offs, have been proposed to solve this problem when data is stored locally. However, for online terrain visualization the problem becomes harder, since data must be transferred in a timely way to be displayed at interactive rendering rates. In such a network environment, the dominant delay comes from the network, and the graphical quality becomes dependent on the payload, bandwidth, and data transfer rate. In order to overcome this handicap, a comprehensive strategy should integrate a hierarchical multiresolution representation of the data with a data compression scheme that allows a progressive transmission of each level of detail. This strategy would enable the client terminal to show an early coarse
*Corresponding author. Email:
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approximation of the terrain model while additional bits are received, in such a way that the bandwidth needed to transmit this information over the network is reduced. Typically, textures are encoded as images. However, DEMs can be encoded using different mechanisms, like an ANSI-standard ASCII characters format, (i.e. USGS 2013), or like a grayscale image format, where each pixel value corresponds to a height value and its horizontal and vertical position is implicitly determined by the indices of this pixel. Using an image format, a unified multiresolution and compression scheme can be applied for both DEM and texture data. Once they are coded like images, it is easy to build a hierarchical multiresolution representation of them as Tiled Pyramids (Figure 1) (Goss and Yuasa 1998, Cline and Egbert 1998), that are variations of Image Pyramids (Tanimoto and Pavlidis 1975) quite used in online terrain applications (Google 2013) because they support progressive transmission in a quite natural way. The image compression schemes based on the Discrete Wavelet Transform (DWT) integrate intrinsically multiresolution and progressive transmission to reconstruct successively higher fidelity versions of an image as data are received, providing not only an efficient overall compression, but also an efficient compression method at every step. Traditionally, tiled-based methods have been the preferred ones for rendering large terrains. If these compression schemes (based on the DWT) are going to be employed in an online terrain visualization application, it would be desirable to make them compatible with the tiled pyramid used by the terrain rendering methods, but from our knowledge, no satisfactory solutions are available at present. To illustrate this point, let us focus on JPEG2000 compression standard (Christopoulos et al. 2000). It is a wavelet-based scheme and has been proved as one of the best image compression algorithms currently available. It allows many formatting alternatives, some related to random access such as tiling. The JPEG2000 tiling scheme segments an image into serial tiles and each tile is independently compressed generating its own image pyramid. The overall result does not suit at all the Tiled Pyramid. Furthermore, tiling artifacts similar to JPEG blocking artifacts occur at tile boundaries at low bit rates and the quality of the image decreases due to a lower peak signal-to-noise ratio. In this paper, we present a novel wavelet compression scheme that replaces the traditional DWT used in analysis and synthesis of images. On the one hand, the proposed scheme uses a novel wavelet-tiled pyramid that replaces the traditional multiresolution pyramid. This new pyramid has been specifically designed to be integrated into wavelet compression schemes specific for online terrain visualization systems. On the other hand,
Figure 1. Tiled Pyramid example with four different resolution levels for a texture (left) and a heightmap (right).
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the wavelet analysis and synthesis processes of the DWT are modified, in order to allow efficient transmission, reconstruction, and rendering of terrain data by using multiresolution tiled pyramid techniques. The method is applicable for both lossy and lossless compression of terrain data. While a restricted description and some preliminary results of this method were presented in a previous work (Olanda et al. 2011), in this paper we present a general description, as well as a comparative study of the proposed method with other current techniques. The results show that the proposed scheme significantly improves the compression ratio of both lossy and lossless coding, reducing the storage space and the required transmission bandwidth, and providing a better visual quality of the terrain model rendered. The rest of the paper is organized as follows: Section 2 gives an overview of related work in online terrain rendering domain. Section 3 describes the terrain data organization and rendering. Next, Section 4 discusses three previous alternative compression strategies based on the JPEG2000 standard. In Section 5, we present the proposed solution and how to integrate it into the JPEG2000 algorithm. Section 6 shows the comparative study of the different strategies considered, and, finally some conclusions are given in Section 7. 2. Related work In this section, we give a brief overview of previously published works related to terrain data compression for efficient transfer over the network and interactive rendering. A more thorough description of other aspects of online terrain visualization can be found in Pajarola and Gobbetti (2007). The implementation of online terrain visualization applications requires, on the one hand, multiresolution techniques to render the geometry and texture simplifications of the terrain in a view-dependent way. On the other hand, it requires a progressive compression scheme for efficiently streaming the geometry and texture data from the systems serving the database to the rendering clients. Many multiresolution algorithms focused on the geometry aspects of the terrain visualization have been proposed . The early works used a CPU-algorithm for fine-grained updates to the terrain mesh (Pajarola and Gobbetti 2007). More recently, the impressive improvement in graphics hardware shifted the bottleneck from the GPU to the CPU. For this reason, the focus has shifted from fine-grained levelof-detail (LOD) to faster block-based LOD techniques (Pajarola and Gobbetti 2007, Bösch et al. 2009). Most of multiresolution texture researches have been targeted to developing methods for fitting large massive textures into small memory spaces. Some works propose LOD structures like texture clipmaps (Tanner et al. 1998), but texture tiling is usually preferred. The tiled pyramid described by Cline and Egbert (1998) or Döllner et al. (2000) is an efficient implementation that exclusively provides those textures strictly necessary for the point-of-view currently displayed, facilitating data storage and streaming. This multiresolution hierarchical structure (the texture tiled pyramid) imposes a mutual interdependence between textures and geometry for quality control and tuning (Döllner et al. 2000, Hwa et al. 2005, Schneider and Westermann 2006). Starting from this observation, Hayat et al. (2008) present a singular method for the synchronized integration of the DEM and the texture into a single unit, through reversible JPEG2000-based blind data hiding. As terrain data sets have become larger, the dominant delay in an online terrain rendering system has shifted to network latency. Recent approaches combine multiresolution schemes with data compression methods to reduce data transfer bandwidth and
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memory footprints (Gobbetti et al. 2006, Bettio et al. 2007, Hayat et al. 2008, Bösch et al. 2009, Dick et al. 2009, Lindstrom and Cohen 2010, Durdević and Tartalja 2013). Compression techniques based on DWT, coupled with statistical coding schemes that maximize compression, have become popular in online terrain rendering applications (Kim and Ra 2004, Losasso and Hoppe 2004, Gobbetti et al. 2006, Bettio et al. 2007, Hayat et al. 2008, Bösch et al. 2009). These compression algorithms rely on the multiresolution nature of the DWT to create multiple LOD for the terrain tessellation adjustment in a view-dependent fashion. They also provide high compression rates, progressive transmission, and random spatial access. Among them, the JPEG2000 standard compression scheme (Christopoulos et al. 2000) should be emphasized. As an example, the JPEG2000 standard was used for 3D geometric objects compression and transmission in Lin et al. (2007). Furthermore, wavelet image compressors can be performed in part or entirely on the GPU, to improve their performance (Wong et al. 2007, Tenllado et al. 2008, Balevic 2010, van der Laan et al. 2011). The JPEG2000 algorithm has also been implemented on the GPU (Park et al. 2009, Weib et al. 2013), improving its performance. These compression techniques based on DWT can be effective in tile-based interactive methods (Kim and Ra 2004, Gobbetti et al. 2006, Bettio et al. 2007, Yusov and Turlapov 2008, Bösch et al. 2009) or for networked systems (Gioia et al. 2004, Kim and Ra 2004, Bettio et al. 2007, Royan et al. 2007). Nevertheless, none of these works efficiently combine wavelet compression and tiled pyramids into an online terrain visualization framework. 3. Data organization and rendering We propose a wavelet multiresolution scheme tailored to tile-based terrain rendering. The internal data structure used for both the DEM and the texture information organization is a tiled pyramid, similar to the ones used in previous works (Schneider and Westermann 2006, Bösch et al. 2009, Dick et al. 2009, Durdević and Tartalja 2013). This hierarchical data structure is used not only to organize the terrain information but also to perform multiresolution rendering and progressive transmission. A Tiled Pyramid, like the ones shown in Figure 1, can be defined as a full and complete quadtree (Döllner et al. 2000)) with the leaf nodes corresponding to the original data. After the original terrain data has been partitioned into a set of regular tiles (rectangular non-overlapping blocks), for each tile a node is created and a multiresolution tile quadtree is constructed in a bottom-up fashion, merging nodes and down-sampling data. This process generates a multiresolution hierarchy for the terrain data set, with several LOD of the terrain region split into a set of fixed-size tiles, where 2 × 2 adjacent tiles on each level are exactly covered by one tile on the next coarser level. In every frame, the set of tiles of the tiled pyramid needed to render the scene depends of the current point of view. This set is determined by traversing the tiled pyramid structure from the top level to the down level, using a recursive procedure to find those offspring tiles that fulfills two conditions: they intersect the camera's view frustum, and their screenspace error is below a given threshold. The Tiled Pyramid allows to perform progressive refinement and transmission of the terrain data over the network. Initially, a lower resolution tile is transmitted. If more resolution is needed for a certain region, then this tile is replaced with the next level of resolution tiles, repeating this process until the required visual quality at every point of the terrain surface is reached.
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Figure 2.
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Cracks along adjacent tiles’ edges.
In order to reduce the time needed to display a terrain region, each tile can be downloaded and displayed in an independent way. However, these independent processes can produce some visual artifacts: cracks and texture artifacts, that can appear among two adjacent tiles with a different LOD (these visual artifacts can also appear among adjacent tiles with the same LOD when they have been lossy compressed). Figure 2 shows an example of cracks due to adjacent tiles with different LOD. Similar visual artifacts occurs with neighboring terrain tiles textures. An example of these artifacts is shown in Figure 3. The main challenge for the tiled pyramid strategy is to ensure that the tile is seamlessly stitched (for both, the DEM and the texture), and the boundaries are diluted enough
Figure 3.
Texture visual artifacts along adjacent tiles’ edges.
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to prevent popping artifacts. Nevertheless, the mesh continuity can be properly achieved by either performing on-the-fly adjustments at runtime, or by imposing constrains in the triangulation model (Pajarola and Gobbetti 2007). The texture continuity can be achieved by using extended textures (which contains adjacent tiles pixel values) or texture morphing. 4. Data compression strategies For comparison purposes, we have implemented not only the proposed compression scheme, but also three different schemes that are (directly or indirectly) based on the JPEG2000 standard compression scheme. In this section, we present these three different compression schemes. The JPEG2000 standard is a wavelet-based compression scheme, and it offers some important capabilities, such as, multiresolution scalability, random access (for both, spatial and frequency domains), high compression ratio, progressive decoding, progressive transmission, lossless and lossy compression in a single compression architecture, etc. These features could make the standard JPEG2000 algorithm a good progressive compression candidate scheme for online terrain visualization applications. Nevertheless, it does not satisfy all the conditions for online terrain rendering systems. Particularly, although the JPEG2000 standard is well suited to the Image Pyramid, it is not well suited to the Tiled Pyramid (as shown below). 4.1. Strategy 1: no information reuse The first strategy considered is the one usually used in terrain visualization applications like Google Earth, Microsoft Bing Maps or NASA WorldWind. Two different types of Tiled Pyramids are defined, one for textures and another one for DEMs. In both cases, each tile is compressed as an isolated image using the JPEG2000 compression scheme (although any other compression algorithm could be used) in such a way that they can be transmitted and decompressed in an independent way, without using information of tiles belonging to lower levels of resolution (that have been previously transmitted). This process is done independently for both textures and heightmaps data. No information is reused in this strategy; so, the total amount of data of the whole Tiled Pyramid involves an overhead factor of approximately 33% with respect to the original data (the higher resolution level of the Tiled Pyramid) (Goss and Yuasa 1998), which reduce the achievable compression rates and cause extra latency. This overhead could be avoided by reusing previously transmitted data, as it is proposed in the other strategies considered. 4.2. Strategy 2: JPEG2000 tiling The second strategy uses the JPEG2000 standard tiling process to split textures and DEMs in several smaller images (tiles) that are compressed and transmitted in an independent way. Every tile generates its own Image Pyramid, as deduced in Figure 4. In this process, first the image color components are transformed to YCbCr components. Then, the image is split into tiles and the wavelet transform is applied to each tile in an independent way. After that, the resulting coefficients of each sub-band are quantized and assembled into code-blocks. Finally, the code blocks are coded individually by entropy coders, as shown in the upper part of Figure 4.
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Figure 4.
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JPEG2000 standard scheme with tiling: Compression(top), Reconstruction(bottom).
In the decompression scheme, the inverse process is followed, as shown in the lower part of Figure 4. We will denote the tiles generated by this JPEG2000 compression scheme as JPEG2000 tiles (JTiles), in order to avoid confusion with the tiles used in a Tiled Pyramid. The main drawback of this scheme is that the number of JTiles generated at every resolution level is always the same, while its size decreases, as shown in Figure 5. Therefore, this scheme does not fit the tile division created in a Tiled Pyramid (the one shown in Figure 1), where the number of tiles decrease and its size remains constant. Nevertheless, it is possible to combine several JTiles to obtain every equivalent tile of the Tiled Pyramid. Also, they can be grouped and transmitted together over the network.
Figure 5.
Strategy 2, JTiles division of the Image Pyramid.
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4.3. Strategy 3: JPEG2000 without tiling The third strategy considered consists of using the JPEG2000 standard without employing the tiling feature, so that no subdivision into tiles is applied to the Image Pyramid. The JPEG2000 standard offers other mechanisms, in addition to tiling, to support spatial random access (thanks to the independent coding of the code-blocks and the packetized structure of the codestream (Christopoulos et al. 2000)). These other mechanisms can be used to decompress terrain regions equivalents to a tile of the Tiled Pyramid in an independent way. Nevertheless, despite the fact that the JPEG2000 standard employs wavelet and scaling functions with reduced compact support, visual artifacts can appear at the frontiers of regions that are independently reconstructed, as shown in Section 6. This is due to the fact that Strategy 3 uses different information in the analysis and synthesis processes. In the analysis process, all the image data are used to generate all the wavelet coefficients, but in the synthesis process (in order to reconstruct a tile of the Tiled Pyramid in an independent way) only the coefficients placed inside the region matching the tile are used to reconstruct this terrain region. That is, the neighboring coefficients that were used in the analysis process are not used in the synthesis process. The compression/decompression scheme of this strategy is the same shown in Figure 4, except for the fact that now the tiling process is not used. 5. A new wavelet compression scheme We propose to replace the traditional wavelet multiresolution analysis used in every wavelet compression scheme by a new one that is well suited to the tiled pyramid, fitting the analysis and tiling processes. The new wavelet analysis process decomposes data following a hierarchical structure, called ‘wavelet tiled pyramid’, in such a way that every tile of the tiled pyramid can be independently reconstructed with no dependencies on other neighbor tiles. It can be integrated in any wavelet compression scheme in order to adjust it to online terrain visualization applications needs. A wavelet analysis example following this new scheme is shown in Figure 6. This figure illustrates each of the steps of the proposed analysis process that is recursively repeated. (i) Before a new step of decomposition of the wavelet transform is applied, the image is split into several tiles of fixed size, as it is shown in the two upper images of Figure 6 (the wavelet compression algorithms, as JPEG2000 standard does, initially split the image into tiles only once). (ii) Then, one level of the analysis process is computed on the data of each tile, which generates four coefficient sub-bands for every tile, named LL (horizontally and vertically lowpass), HL (horizontally highpass and vertically lowpass), LH (horizontally lowpass and vertically highpass), and HH (horizontally and vertically highpass). The second row of images in Figure 6 shows these four subbands generated for each tile. (iii) All low-pass sub-bands (LL) are merged into a lower resolution version of the image, after which the procedure is repeated (as shown in the third and fourth rows of images of Figure 6) until the image size is smaller than the tile size. In order to reconstruct these tiles, the wavelet synthesis process is applied in a progressive way, using the inverse DWT module properly modified to apply only one
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Figure 6.
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Four first steps of the image decomposition process.
step. In order to reconstruct the data of a particular tile, one step of the synthesis process is applied to its detail coefficient sub-bands HL, LH, and HH in conjunction with the corresponding data of the father tile (used as LL sub-band). Once the tile has been reconstructed, the resulting data can be used as the coarse approximation to reconstruct any children tile, and so on. This tile reconstruction will not produce visual artifacts in the region frontiers because the same set of coefficients will be applied in the synthesis and analysis processes of the wavelet transform, avoiding the use of coefficients that belong to neighboring tiles in both
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cases (unlike, for example, the JPEG2000 standard scheme used in strategy 3). The modifications introduced in the analysis process will also allow the number of generated tiles to fit in the Tiled Pyramid. That is, the size of the tiles generated will be the same in all the resolution levels of the Tiled Pyramid, and the number of tiles will decrease at each level of resolution (unlike, for example, the JPEG2000 standard tiling scheme used in strategy 2). Additionally, the resulting data generated in the tile synthesis is reused at the next child tiles. That means that there will not be data overhead in the coding process of the tiled pyramid data (unlike the traditional coding scheme employed to compress the tiled pyramid information, used in strategy 1). 5.1. Strategy 4: JPEG2000 adapted to the new wavelet-tiled pyramid The proposed strategy is also based on the JPEG2000 standard, although it is properly modified to fit the requirements of terrain visualization applications. In order to solve the problems of the previous strategies, the last strategy replaces the analysis and synthesis processes of the wavelet transform included in the JPEG2000 standard by the new wavelet analysis and synthesis processes described above. The modified compression scheme is shown in the upper part of Figure 7. This scheme is similar to the one used by the JPEG2000 standard, but the image tiling process and the DWT application are different. This new compression scheme consist of the following steps: first, the image is transformed from the RGB color space to YCbCr color space, leading to three components that are handled separately. Second, the image is split into tiles. Third, one analysis step is applied to every tile. Fourth, the detail coefficients (corresponding to HL, LH, and HH sub-bands) are quantized to reduce the number of bits required to code these coefficients. They are grouped into code-blocks and encoded by a context-driven binary arithmetic coder. Fifth, the low-pass coefficients (LL) are merged into a new low-resolution version of the image. Steps 2, 3, 4, and 5 are repeated until the low-resolution version of the image generated in Step 5 is smaller than the tile. In order to reconstruct these tiles, the inverse process takes place in a progressive way. The decompression process consists of the same steps as the JPEG2000 standard scheme, as shown in the lower half of Figure 7. However, the inverse DWT module is properly modified to apply only one step every time.
Source image
Color transf.
Recombine LL
Tiling
Reconstructed image / Tile
DWT (1 step)
Entropy encoding
Quantization
Inverse color Tr.
Entropy decoding
Inv. DWT (1 step)
Inverse quantization
Compressed image data
Figure 7. JPEG2000 modified scheme (strategy 4): Compression(top), Reconstruction(bottom). Differences between it and the original JPEG2000 scheme have been highlighted.
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These modifications increase the time required to compress the data with respect to the original JPEG2000 algorithm, as shown below, mainly due to the LL sub-bands recombination. Nevertheless, the compression of the data is done off-line and, therefore, it does not affect the performance of the real-time terrain visualization. The time requiring for decompressing the data is similar to the original JPEG2000 algorithm because the same decompression process is done. The main difference is that all the inverse DWT steps were applied consecutively in the original scheme, and now they are applied in an independent way. 6. Evaluation and testing We have implemented a generic terrain visualization application to compare the four data compression strategies considered. This application performs a real-time fly over different terrain data sets using different visual quality parameters. The application allows taking top-view photos and user point-of-view photos of the virtual terrain surface and storing them for analysis. The terrain data used for this application consists of a set of terrain textures and DEMs of the Region of Valencia (Spain) that have been compressed using the four compression strategies. This terrain database is composed by a global terrain texture image of 262,144 × 262, 144 pixels that is equivalent to an uncompressed database of 192 GB, and a heightmap image of 2263 × 3379 pixels that is equivalent to an uncompressed database of 15 MB. The global texture image and DEM have been split in regular tiles of lower size. We have performed the following tests on the same images after being compressed using the considered schemes: ● ● ● ●
Visual artifacts. Lossless compression ratio. Lossy compression root mean square error. Compression/decompression speed tests.
6.1. Visual artifacts Terrain visualization systems with online databases need to reconstruct every tile of the Tiled Pyramid in an independent way. When Strategy 3 is used (JPEG2000 without tiling) to reconstruct a terrain region in an independent way, visual artifacts will appear in the frontiers of these regions. This test checks visual artifact impact in both, a qualitative and a quantitative way. In order to achieve this goal, terrain images have been lossless compressed using the considered compression strategies and reconstructed by regions in an independent way. Figure 8 shows a representative example. Figure 8a shows the user point of view in a certain reference frame. Figure 8b shows the terrain data set (at high resolution) corresponding to the terrain region viewed by the user at that moment. Figures 8c and 8d) show the tiles used from the Tiled Pyramid at that user point of view by Strategy 3 and 4, respectively. These tiles have been selected using a measure based on distance. Figure 8c shows visual artifacts in the frontiers between terrain regions of the same level of resolution. These visual artifacts do not appear in Figure 8d. The visual differences have been emphasized by red ellipses. Strategies 1 and 2 provide results similar to the ones in Figure 8d.
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(a)
Figure 8.
(b)
(c)
(d)
Visual artifacts image examples.
Table 1.
Version Version Version Version Version
Image Figure 8 RMSE.
0 1 2 3 4
Strategy 3 RMSE
Strategy 4 RMSE
83.10 71.76 58.17 38.03 13.84
82.51 70.61 55.29 34.14 0.00
In order to evaluate the visual quality in a quantitative way, five versions of the terrain surface shown in Figure 8 have been reconstructed by tiles of the same resolution in an independent way, and their root mean square error (RMSE) have been measured in relation to the high resolution terrain surface. Table 1 shows the results for the Strategies 3 and 4. The results provided by Strategies 1 and 2 are similar to the ones provided by Strategy 4. Version 0 corresponds to the lowest level of resolution, and version 4 corresponds with the highest resolution reconstruction. The error using the Strategy 3 is greater than the error obtained when others strategies are used, and it occurs for all the versions. Moreover, Strategy 3 does not achieve a perfect reconstruction of the image at high resolution, unlike the rest of strategies. This behavior is due to the fact that Strategy 3 has used all image data in the analysis process, but only the transmitted tile coefficients have been used in the synthesis process (when also the neighbor data would be needed). These visual artifacts are extended in each synthesis process of the wavelet transform, causing an imperfect reconstruction of the complete image. As a result, we can conclude that Strategy 3 is not valid for terrain visualization applications due to these visual artifacts, resulting in a low quality terrain visualization. 6.2. Lossless compression ratio Terrain data size is an important factor, since it affects the amount of storage, network bandwidth, and time required to transmit the data. In order to analyze the compression rate that each compression scheme can reach, a set of different terrain images have been compressed using different tile sizes. Some examples of these images are shown in Figure 9, where the A image refers to a heightmap image and the B, C, and D images refer to a texture image. In order to measure the compression rate, we have used the Equation (1).
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Figure 9.
(a)
(b)
(c)
(d)
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Four images used for compression test: one heightmap and three textures.
Crate ¼
Uncompressed image size Compressed image size
(1)
The numerator of this fraction corresponds to the size of the uncompressed image at full resolution, and the denominator corresponds to the size of the compressed image ready to generate the Tiled Pyramid. The precinct size used follows the JPEG2000 standard recommendations (values between 16 × 16 to 64 × 64 pixels) and we have chosen the greatest size as possible to achieve the best compression ratio. Table 2 shows the compression ratio provided by the four considered strategies (labeled as S1, S2, S3, and S4) when applied to the images in Figure 9, with several tile and precinct sizes. Table 2 shows that the compression ratios provided by Strategies 3 and 4 are similar, and better than those achieved by Strategies 1 and 2. This is due to the fact that Strategy 1 does not exploit redundancies among separated LODs. So, it has to transmit different images for each level of resolution of the Tiled Pyramid, and the compressed image size will be not only the high level resolution image compressed size, but the addition of the size of each image with a different resolution. On other hand, Strategy 2 treats each tile like an isolated image, which limits the amount of data available for the compression algorithm and, therefore, the compression ratio reached with this strategy. Table 2 shows some empty cells for Strategy 2, since the maximum number of JTiles allowed by the JPEG2000 standard is 65,535. Therefore, it is not possible to compress images C and D using JTiles of size 32 × 32 pixels, nor image D using JTiles of size 64 × 64 pixels, because it exceeds this maximum number of JTiles. For Strategy 3, no tiles have been used. In order to illustrate the results in a more graphical way, Figures 10 and 11 show the compression ratio results for images A and D presented in Table 2. This figures show that Strategies 3 and 4 achieve similar compression ratios. For lower tile sizes, Strategy 2
14 Table 2.
Compression ratio.
Tile size
Prec. size
32 × 32
16 × 16
Compr. Image A Image B Image C Image D scheme (2048 × 2048) (4096 × 4096) (8192 × 8192) (16,384 × 16,384) S1 S2 S3 S4
9.09 11.52 15.67 15.67
1.24 1.37 1.61 1.61
1.49
1.59
1.98 1.98
2.16 2.16
S1 S2 S3 S4
13.32 15.52 18.73 18.73
1.29 1.63 1.71 1.71
1.56 2.00 2.12 2.12
1.71
128 × 128 64 × 64
S1 S2 S3 S4
13.91 18.73 19.70 19.70
1.31 1.72 1.74 1.74
1.59 2.14 2.18 2.18
1.75 2.34 2.39 2.39
256 × 256 64 × 64
S1 S2 S3 S4
13.98 19.63 19.83 19.83
1.31 1.74 1.74 1.74
1.59 2.17 2.18 2.18
1.75 2.39 2.40 2.40
64 × 64
32 × 32
2.33 2.33
S1: No information reused
S2: Jpeg2000 with tiling
S3: Jpeg2000 without tiling
S4: New scheme
Compression ratio
20.00 18.00 16.00 14.00 12.00 10.00 8.00
Figure 10.
64 × 64
128 × 128 JTile size
256 × 256
S1: No information reused
S2: Jpeg2000 with tiling
S3: Jpeg2000 without tiling
S4: New scheme
2.50 2.30 2.10 1.90 1.70 1.50
Figure 11.
32 × 32
Image A compression ratio.
Compression ratio
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32 × 32
Image D compression ratio.
64 × 64
128 × 128 JTile size
256 × 256
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achieves worse compression ratio than Strategies 3 and 4, but for higher tile sizes the compression ratio achieved is similar. Strategy 1 is the worst strategy, achieving a low compression ratio. These results are similar for the other images. As a result, we can conclude that Strategy 4 provides the best lossless compression ratio without producing visual artifacts. 6.3. Lossy compression root mean square error (RMSE) Lossy compression adds errors in each analysis step of the wavelet transform, degrading the reconstructed image at each reconstruction step. Nevertheless, since simplified DEMs and textures on coarse levels in the tiled pyramid already present some data loss, terrain visualization applications use lossy compression schemes to further reduce the size of the terrain data and the transmission time. In order to study which compression scheme provides the highest visual quality when using lossy compression, a set of images have been compressed using different bit rates. These images have been decompressed using all the information of each level of the Tiled Pyramid. The RMSE respect to the original image has been measured. Figure 12 shows four zoom images of a region of the image shown in Figure 9c compressed using lossy compression, and subsequently reconstructed using all the
Figure 12.
(a)
(b)
(c)
(d)
Lossy compression and reconstruction (image zoom of Figure 9c, 0.05 bpp).
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Table 3.
R. Olanda et al. RMSE – Lossy compression.
bpp
Strategy 1 RMSE
Strategy 2 RMSE
Strategy 3 RMSE
Strategy 4 RMSE
0.05 0.10 0.15 0.25 1.00 2.00 3.00 4.00
30.28 25.33 21.89 17.67 7.54 4.04 2.58 1.88
35.80 27.52 22.82 17.47 6.72 3.39 2.09 1.49
27.99 22.83 19.73 15.05 5.98 3.02 1.88 1.38
28.22 23.03 19.95 15.26 6.03 3.07 1.91 1.40
information of the Tiled Pyramid. Concretely, this Figure shows the image results for a compression ratio of 0.05 bits per pixel (bpp). The image size is 2048 × 2048 pixels, using a tile size of 128 × 128 pixels (except for Strategy 3, where the tiling process was not applied) and a precinct size of 64 × 64 pixels. Figure 12a shows the results of applying Strategy 1, Figure 12b shows the results for Strategy 2, Figure 12c for Strategy 3, and Figure 12d for Strategy 4. Figure 12a has a lower visual quality than Figure 12c and d. It can be observed in some elements presented in the image like the roofs and the cars. Figure 12b has the lowest visual quality of the images considered. Unlike in the other images, a block effect can be observed in this image. It is also worth mention that no noticeable differences can be observed between Figure 12c and d. Table 3 shows the lossy compression results in a quantitatively way. It shows the RMSE value obtained for the considered strategies using different compression ratios for the image, including the compression ratio of 0.05 bpp showed in Figure 12. Table 3 shows that for different bpp Strategies 3 and 4 obtain image reconstructions of similar visual quality, although Strategy 4 applies a tiling process and no tiles have been used for Strategy 3. Their visual quality is higher than the one obtained by Strategies 1 and 2. Table 3 also shows that Strategy 1 is better than Strategy 2 for lower bpp values, but it is worst for higher values of bpp. This is due to the fact that Strategy 2 suffers a smaller block effect as bpp is increased. As a result, we can conclude that Strategy 4 provides similar lossy compression rates than Strategy 3 (furthermore, it does not provide visual artifacts). 6.4. Compression and decompression speed The process of recombining the LL sub-bands in the modified JPEG2000 algorithm (Strategy 4) increases the time needed to compress the terrain data with respect to the original JPEG2000 algorithm. We have measured this time increment. Figure 13 shows a comparison of the percentage of average time compression for different images of size 16,484 × 16,384, using the original and the modified JPEG2000 compression scheme. The compression time for the modified scheme is always greater than the original scheme, but as tile size is greater, the compression time using the modified scheme approaches the original scheme. This is due to the low number of the needed recombining processes that take place in the image compression process.
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Figure 13.
Jpeg2000 modified scheme
160 140 120 100 80 60 40 20 0 32 × 32
64 × 64
128 × 128 JTile size
256 × 256
JPEG2000 original scheme and modified scheme compression time comparison.
Nonetheless, the terrain visualization performance is unaffected by this time increment, because the compression of the terrain data is performed off-line. On other hand, Figure 14 shows the comparison (in percentage) of the average time decompression of these images, using the original and the modified JPEG2000 compression schemes. The decompression times are similar. It is due to the fact that both schemes use the same decompression process. The main difference is that all the inverse DWT steps were applied consecutively in the original scheme, and in the new scheme they are applied in an independent way. 7. Conclusions In this paper, we have presented a new wavelet compression scheme that replaces the traditional multiresolution pyramid by a new wavelet-tiled pyramid. The new method can be integrated in most of the relevant compression schemes based on DWT, making them to properly fit tile based terrain rendering approaches. In order to evaluate the performance of the proposed method, we have modified the JPEG2000 algorithm to integrate the new wavelet analysis method, and we have evaluated it on a typical online terrain visualization application. For comparison purposes, we have also implemented three additional compression strategies based on the JPEG2000 standard algorithm. The performance evaluation results show that the proposed compression scheme perfectly fits the Tiled Pyramid structure usually used to organize data in online terrain Jpeg2000 original scheme
Decompression time (%)
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Compression time (%)
Jpeg2000 original scheme
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110 105 100 95 90 32 × 32
Figure 14.
Jpeg2000 modified scheme
64 × 64
128 × 128 JTile size
256 × 256
JPEG2000 original scheme and modified scheme decompression time comparison.
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visualization applications. It reuses previous information transmitted, reducing the data to be transmitted (compared to the standard approach) about a 30%. Also, it can reconstruct terrain regions in an independent way, avoiding visual artifacts in the borders of these regions. Finally, it obtains better lossless and lossy compression ratios, as well as better visual quality. The other considered compression strategies, on the contrary, or they do not reuse previous information transmitted, so they need to transmit more data over the network (Strategy 1), or they obtain a lower compress ratio and visual quality (Strategy 2), or they produce visual artifacts at the region borders when these regions are reconstructed in an independent way (Strategy 3). These results show that the new wavelet analysis method can significantly improve the performance of online terrain visualization applications like 3D online games, virtual world visualization, GPS navigation, etc. Acknowledgments This work has been jointly supported by the Spanish MICINN and the European Commission FEDER funds, under grant TIN2009-14475-C04.
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