Linköping University | Department of Electrical Engineering Master’s thesis, 30 ECTS | Information Coding 2020 | LIU-ISY/ISY-A-EX-A--20/5344--SE Evaluating Image Compression Methods on Two Dimensional Height Representations Oscar Sjöberg Supervisor : Harald Nautsch Examiner : Ingemar Ragnemalm External supervisor : Filip Thorardsson Linköpings universitet SE–581 83 Linköping +46 13 28 10 00 , www.liu.se Upphovsrätt Detta dokument hålls tillgängligt på Internet - eller dess framtida ersättare - under 25 år från publicer- ingsdatum under förutsättning att inga extraordinära omständigheter uppstår. Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner, skriva ut enstaka ko- pior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning och för undervis- ning. Överföring av upphovsrätten vid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av dokumentet kräver upphovsmannens medgivande. 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For additional information about the Linköping University Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its www home page: http://www.ep.liu.se/. © Oscar Sjöberg Abstract The need for compression and sparse representation varies within the fields of com- puter science. However, a field that has always benefited, and been an integral part of the compression vocabulary is the digital image. There are however many things that can be done with data structured in a two dimensional raster. In this report standard lossy image compression techniques are evaluated on a DTM (Digital Terrain Model) to assess their applicability in the height domain. Tests were performed using different open source soft- ware to increase repetability. The best performing codec, JPEG2000, was also introduced into a 3D graphic context, enabling subjective evaluation of the gain of smaller disk space to the higher resolution. The JPEG2000 also permitted the data to be loaded in a more efficient manner, thanks to the progressive capabilities of the codec. Acknowledgments This master thesis hadn’t come to exist without all the inventiveness and positive energy rubbed of from the different people I’ve encountered during my studies here at Linköping, both at the university and at the Vricon office, so I owe my thanks to many! However, in the pursuit of brevity, avoiding a harangue, I want to direct acknowledgement to the people di- rectly responsible for this report. Thus, big thanks to both my examiner, Ingemar Ragnemalm, and supervisor, Harald Nautsch, for your guidance provided during the project. The mas- termind behind the thesis, Filip Thorardson, has also been eager to respond to questions and thereby deserves many thanks. Last but not least I want to thank my friend Simon Kantedal, not only for giving structural feedback and reading this report but also for being a source of inspiration and a motivational force all through my studies at Linköping University. iv Contents Abstract iii Acknowledgments iv Contents v List of Figures vi List of Tables vii 1 Introduction 1 1.1 Motivation . 1 1.2 Aim............................................ 1 1.3 Research questions . 2 1.4 Delimitation . 2 2 Theory 3 2.1 The application . 3 2.2 The two dimensional height raster . 4 2.3 Compression of Images . 5 2.4 JPEG . 8 2.5 WebP . 11 2.6 JPEG2000 . 14 2.7 Metrics for comparison . 19 3 Method 20 3.1 Compressors . 20 3.2 Quality parameter . 20 3.3 Sub-division in frequency domain . 21 3.4 Height Raster Pre and Post Processing . 21 4 Results 23 4.1 Height data compression . 23 4.2 In the geometric context . 28 5 Discussion 30 5.1 Literature Criticism . 30 5.2 The Evaluating Metrics . 30 5.3 Others Results . 30 5.4 Other Compression Schemes . 31 5.5 The work in a wider context . 31 6 Conclusion 32 Bibliography 34 v List of Figures 2.1 Vricon Explorer . 4 2.2 Conceptualisation of a DWT subband cascaded filter response . 7 2.3 JPEG compression scheme . 8 2.4 DCT Basis and the zigzag deconstruction pattern . 9 2.5 Example of quantisation tables used in JPEG quantisation step . 9 2.6 JPEG box artefacts . 12 2.7 WebP compression scheme . 12 2.8 RIFF internal lay out . 13 2.9 JPEG2000 compression scheme . 14 2.10 Dyadic tree structure . 15 2.11 The EBCOT paradigm . 16 2.12 Partitioning of subbands, precincts and code-blocks in JPEG2000 . 17 2.13 Quad-tree structure of the stripes and their bit-plane, in a code-block. 17 2.14 The JPEG2000 marked up codestream . 18 4.1 PSNR given bits/pixel, where jp2 corresponds to JPEG2000, jpg to JPEG and webp toWebP............................................ 24 4.2 SSIM given bits/pixel, where jp2 corresponds to JPEG2000, jpg to JPEG and webp toWebP............................................ 25 4.3 PSNR given bits/pixel – high compression rate – where jp2 corresponds to JPEG2000, jpg to JPEG and webp to WebP . 25 4.4 SSIM given bits/pixel – high compression rate – where jp2 corresponds to JPEG2000, jpg to JPEG and webp to WebP . 26 4.5 Evaluating PSNR and SSIM for different block sizes in the JPEG codec . 26 4.6 PSNR and SSIM for different quality layers in the JPEG2000 codec . 27 4.7 JPEG2000 coded data with falling SNR 80, 60, 35 and 15 dB as input . 27 4.8 Comparing PSNR and SSIM between different resolution layers, 3-9, compressed with ratio 0-75. 28 4.9 Display texturised globe in Vricon Explorer: old map to left and new map, JPEG2000, to the right . 29 4.10 Display globe in Vricon Explorer through height shader: old map to left and new map, JPEG2000, to the right . 29 vi List of Tables 2.1 Tabular representation of JFIF format. 11 vii 1 Introduction Compression is a founding block of modern data science on which many, if not all, of the every day media applications are heavily dependent. Video and music streaming, an integral part of modern web services, could not be delivered with the necessary latency and quality demands of the everyday user if compression schemes should be left out of the equation. With these compression methods, data and information can flow more freely and be more accessible to users, independent of the users system. This is also true for the data used in non web based software. By using data more efficiently and take up less disk applications can be made more available. It also gives creators more freedom to freely design and scale their software more aligned with their wishes. This thesis examines the possibilities to use the standard image compression methods on data structured in the same manner, the two di- mensional raster. However, these rasters depicts something completely different than colour, namely heights. 1.1 Motivation So why would one need height data expressed in a two dimensional array? There are several reasons. Representing data in two dimensional arrays, such as raster, comes with a many different useful perks, such as matrix computation for transforms. Nevertheless, saving high quality rasters, without destroying the data, is problematic and uses a lot of disk compared to other data formats. So if this non-colour data, meaning height data, could be compressed in a similar manner as their chromatic counterpart this would greatly benefit the quest for the sparse representa- tion of data. The motivating factor for this refactoring of height data is to be able to introduce the compressed raster in the graphical tool Vricon Explorer, which is described further in 2.1. 1.2 Aim Two dimensional data can be used in a set of different applications, not only for representing colours in image and video. The heights in this application are used for a geometric purpose, pushing vertexes in a three dimensional object, creating geometric variations on a surface. 1 1.3. Research questions The object in question is the earth, the globe, and the heights are the actual heights, meters above (and under) sea level. The aim is thus to represent the vertex positions of this three dimensional model as accurately and aesthetically pleasing as possible, while using up the smallest storage space possible. 1.3 Research questions Image compression schemes have been investigated thoroughly over the decades, turning them inside out and back again, to prove and disprove their superiority when compressing different types of image data. Such as real image data [12], [14] , medical applications [18][21] and many more.