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LizardTech, США
Email: rburley@lizardtech.com
ТЕХНОЛОГИЯ MRSID ДЛЯ СЖАТИЯ, ХРАНЕНИЯ И УПРАВЛЕНИЯ БОЛЬШИМИ МАССИВАМИ РАСТРОВЫХ И ГЕОПРОСТРАНСТВЕННЫХ ДАННЫХ LIDAR
На сегодняшний день технология LizardTech® позволяет решать проблемы хранения и управления большими массивами геопространственных данных. Благодаря сенсорам высокого разрешения, стали доступными многоспектральны данные и данные LiDAR
Фирма LizardTech разработала технологию MrSID, позволяющую достичь более высокого уровня компрессии, чем любой другой существующий метод. В статье рассматривается концепция сжатия растровых, изображений, MrSID технология и ее особенности. Технология сжатия MrSID ориентирована на издательство, профессиональную картографию и другие области, где используются растровые изображения высокого разрешения, можно создавать архивы растровых изображений высокого качества.
Ryan Burley
LizardTech, USA
Email: rburley@lizardtech.com
MRSID TECHNOLOGY FOR STORING AND MANAGING LARGE RASTER AND LIDAR GEOSPATIAL DATASETS
SUMMARY
For over a decade, the MrSID® technology from LizardTech® has been the GIS industry’s leading solution to the problem of storage and management of large geospatial datasets. Today, as the precision of sensors increases and as new data forms such as multispectral and LiDAR become more widely available, the need for advanced compression technology such as MrSID continues to grow.
In this white paper, LizardTech introduces you to the concept of compression, MrSID technology, and the features that the MrSID format brings to your applications and workflows
I. The Need for Data Compression
Aerial and satellite imagery have been used by the geospatial community for decades. It is only in recent years, however, that such imagery has truly become critical, highly accurate, and ubiquitous: for this we can credit the Katrina disaster
response efforts, worldwide counterterrorism initiatives, technical achievements in optics and signal processing, and browser-based mapping frameworks. Unfortunately, as rapid access to such data has become an imperative, organizations continue to struggle with storing, accessing, and exploiting the massive archives of high-resolution data that are so vital. National security agencies, web content providers, and your county government all have the same set of challenges.
Because digital image files are so large, maintaining imagery in its raw, uncompressed form requires immense physical storage resources, and accessing raw data requires high-bandwidth networks and large memory workstations. A typical alternative is to store imagery in compressed form, using file formats like JPEG. Although JPEG versions of the images may enable faster access to lower resolution image overviews, their quality is not suitable for analysis and exploitation work at high resolution. This often leads to the practice of storing multiple versions of each dataset, at different resolutions or compression ratios - one for browsing, one for analysis, and so on. The storage and maintenance problem gets worse, not better.
We know from working with customers such as the United States Geological Survey (USGS) and the National Geospatial-Intelligence Agency (NGA) that today’s geospatial workflows regularly require support for files hundreds of gigabytes in size, storage of the imagery without significant quality loss, access to multiple resolutions or overviews quickly, efficient random access into the file to support arbitrary scene requests, and so on.
For over a decade, the patented MrSID® technology from LizardTech® has been the GIS industry’s leading solution to these problems. Our applications such as GeoExpress® and Express Server® are used by thousands of people every day to encode and deliver imagery. And thousands more use MrSID files in hundreds of applications including ESRI ArcGIS, ERDAS Imagine, and Google Earth.
With the introduction of the MG4™ format, the latest version of the MrSID technology, LizardTech now offers compression for new kinds of datasets like multispectral images and LiDAR point clouds. In this white paper, we will introduce you to MrSID technology: what features it offers, where it can be applied, and how it works.
II. MrSID Technology
What is Compression?
Compression just means making data more compact so it occupies less space, but the word sometimes has negative connotations in our industry: often compressing imagery resulted in degraded data quality. You could have high fidelity or you could save disk space - but not both.
Consider a typical aerial image that is in 8-bit color and is 6,000 pixels wide by 6,000 pixels high. This means the raw data would consist of about 100 megabytes (MB) on disk: 36 million pixels (6,000 x 6,000), with each pixel requiring three bytes (three color bands of one byte each). A common workflow might, in fact, have dozens or even hundreds of such images arranged as tiles to make up a complete mosaic, but let’s just consider the one image.
When the pixels are stored in an uncompressed (raw) form like this, the image data is not compressed at all: the amount of disk space required is equal to the number of bytes needed to represent the pixels (plus some small amount for metadata such as the geospatial positions of the corner points). Geospatial file formats like GeoTIFF store data in this raw, or uncompressed, way: every single pixel is fully represented. Uncompressed formats have the advantage of representing each pixel’s data exactly as it was originally recorded, and so we say the image data is lossless. The obvious disadvantage, of course, is all the disk space you need.
Through the use of various algorithms, however, we can often represent the pixel data in a more efficient form. Intuitively, you can think of it this way: if the data consisted of a sequence of five identical values such as 123 123 123 123 123, you might instead be able to code it using a sort of shorthand notation like 123[5] in which you store the value only once but add a “repeat count” to it. Techniques like this yield data that is compressed - which means less disk space is needed - but the image data is still lossless.
If we push our compression algorithms further, we can find techniques which do not store the data for each pixel exactly but instead store only approximations of the data. Again intuitively, a high precision number like 3.1415, which requires five digits, might be stored as just the single-digit number 3, an 80% reduction in digit space (a 5:1 compression ratio). The JPEG file format, commonly used for small images on the web, uses this sort of lossy compression. The penalty for such lossy compression schemes is that you typically lose image quality: edges might not be as sharp, colors might seem flatter, small artifacts might be introduced. For some less demanding geospatial workflows, this might be acceptable.
In summary, then, we have a spectrum of three kinds of compression and data loss: uncompressed and lossless; compressed and lossless; and compressed and lossy. The naive techniques just described to achieve these kinds of compression will work, but by no means would provide high compression ratios, high image quality, and high performance. To do compression well in the real world, the algorithms need to be designed for specific kinds of data, such as geospatial imagery, and specific kinds of workflows.
MrSID Technology: Quality and Performance
The compression techniques used by MrSID technology provide both high quality imagery and high performance while still meeting our industry’s chall enging workflows.
Image Quality: MrSID technology’s lossless compression yields compression ratios of 2:1 for typical imagery. This means you need only half the storage space and yet still retain your numerically identical, original data.
For further storage savings, MrSID technology’s lossy compression can yield typical ratios of up to 20:1 while still offering a level of image quality that makes the data indistinguishable to the eye for most workflows. We refer to this style of compression as being visually lossless: there is still data loss, but with respect to what the image is being used for, the amount of loss is imperceptible.
Higher compression ratios are, of course, possible. Depending on how much image quality you need to retain, and depending on the type of your original imagery, ratios of 40:1 and beyond can be used.
Encoding Performance: Geospatial datasets can grow to consume terabytes of disk space. Sometimes the dataset is just one large file, but often it consists of hundreds of smaller tiles that, taken together, form a large mosaic. Either way, with many applications the amount of memory required to process and compress such large datasets is prohibitive, requiring the use of server-class hardware or requiring the end user to work with their imagery “piecemeal”, only a subset of the tiles at a time.
MrSID technology is designed to address this problem. With full support for input and output file sizes larger than 2 GB and with support for 64-bit processors, there is virtually no limit to the size of the imagery that can be compressed.
Viewing Performance: Even at a ratio of 20:1, compression of a 20 TB dataset still results in an extremely large (1 TB) MrSID file. Users are often nervous about working with files of that size because many GIS applications will attempt to ingest the entire file, causing excessive and occasionally fatal demands on the CPU and memory. Two aspects of MrSID technology solve this problem.
First, the encoding technique we use creates multiple resolutions of the image within the generated MrSID file. This is similar in effect to the trick of creating image “pyramids”, but the MrSID technique does not create extra files for all the pyramid levels nor incur the corresponding overhead in storage space. Instead, the resolution levels are inherent in the encoding scheme and fully contained within the single MrSID output file itself. These levels are scaled such that each level is one quarter of the previous level: for example, the full image at 1024x1024, then a quarter-scale image at 512x512, then a sixteenth-scale image at 256x256, and so on down to an “icon” or “thumbnail” of typically 32x32. Applications can be instructed to extract
and process to only the level of detail required, without having to decode (and perhaps then manually down-sample) the entire full-resolution image.
In addition to enabling requests for only the resolution level desired, MrSID technology offers selective decompression, which allows applications to request and decode only the scene (geographic area) of interest from the file. Some other file formats and compression schemes, by contrast, require the whole image to be decoded even if only a small part is to be shown on the screen.
Introducing the MG4 Format: The prototype for MrSID technology was developed at Los Alamos National Laboratory in 1992. LizardTech’s subsequent commercial version of the technology was called the MrSID Generation 2 (MG2) format and was introduced in 1998. The next version, the MrSID Generation 3(MG3) format, introduced in 2002, offered improved image quality and key features such as lossless encoding.
After a decade which saw the MrSID format become a de facto industry standard, LizardTech introduced the next generation of the MrSID family. In response to customer demand, we have extended the MrSID format to MrSID Generation 4 (MG4) to support multispectral imagery, enabling users to compress 4-band NAIP data, 8-band Landsat data or even 224-band AVIRIS data, losslessly or with our usual high-quality visually lossless compression. The MG4 format also adds support for alpha bands, enabling users with shapefiles defining the boundaries of their image data to perform more complex mosaicking operations than ever before.
Until now, MrSID technology has only supported raster data - pixels arranged in a very regular, 2D grid - but in the past few years, customers with very large, irregular, 3D elevation datasets have asked us for compression support. With the MG4 format, we have added support for LiDAR point clouds. With LiDAR data, users of the MrSID format get many of the same key features found in our raster compression technology, including lossless and visually lossless compression, and selective decoding.
MrSID technology is available in LizardTech’s suite of applications and tools, ranging from full-featured encoding applications to image servers to lightweight viewers. In addition, through our integration partners, MrSID files are supported in hundreds of GIS applications. Whether you are using older MG2 files in your legacy applications, taking advantage of MG3's lossless files in your current workflows, or have a new need to efficiently encode multispectral raster or LiDAR point cloud datasets, MrSID compression technologies will support your needs.
III. MrSID Technology for Imagery
In this section we describe in more detail some of the features and capabilities of the MrSID technology for raster image data.
Data Types and Formats
The MrSID technology is agnostic with respect to the input file format, as long as the input pixel data meets certain datatype requirements. This means that MrSID files can be generated from a variety of data sources including GeoTIFF, Imagine, and ECW.
The MrSID technology supports most data types used in geospatial raster imagery today: up to 16 bits per sample (signed or unsigned). Raster image data is almost always represented using unsigned integers. Digital elevation models and file formats like DTED, however, often use a signed integer representation, and so to support situations where our users want to compress these sorts of datasets, or perhaps use terrain models as base layers for their visualizations, MrSID supports signed integer data of up to 16 bits. The MrSID technology also supports 1-band grayscale, 3-band RGB, and 1- to 255-band multispectral or hyperspectral imagery.
Image Quality
As discussed above, MrSID technology offers excellent image quality for a given file size target.
- Numerically lossless: This level of compression typically yields a 2:1 compression ratio, for a 50% reduction in storage space. Lossless compression should be used when it is critical that all bits of the original image be preserved. This is the case for archival storage, as well as for uncommon workflows where no possible loss of precision is ever acceptable. You may also wish to use lossless compression when you are generating a “master” image from which other derivative images will be made, as through the MrSID optimization process described below.
- Visually lossless: This level of compression is typically 20:1 for RGB and 10:1 for grayscale imagery. This is the most common level of compression quality used, as it preserves the appearance of the imagery for most workflows, including use of your imagery as a background layer and for many forms of visual analysis and exploitation.
- Lossy: Beyond 20:1, image degradation and artifacts can appear, although often not too significantly until ratios of 40:1 or 50:1. Such lossy quality may be acceptable when the imagery is used only as a background layer for appearance or when the image quality is less important than the storage size or speed, such as for informal visual inspections.
Performance
When considering performance, we usually consider the cost of running some process, such as compression or decompression, in terms of memory usage, CPU usage, and I/O bandwidth. The MrSID technology is designed with these concerns in mind.
- Compression: When dealing with very large images, many image processing algorithms first partition the image into tiles and then process each tile independently. This allows the computation to proceed without slowing down due to excessive paging of memory to disk. However, especially in the case of compression
algorithms, such tiling can introduce artifacts in the resulting image because the algorithms cannot efficiently process cross-tile regions. MrSID technology is specifically designed to process imagery whose size is larger than the amount of RAM available on the machine without resorting to tiling schemes and therefore without introducing any tiling artifacts.
- Decompression: When decompressing imagery, the most common use case is for viewing, which means extracting out scenes - only some subsets or regions of the image are needed at any one time. With the multiresolution support inherent in the MrSID format, the viewing application may first decide the resolution level needed to display the scene at some physical screen resolution and then extract only the resolution levels needed; this significantly improves disk I/O time and lowers the amount of imagery the CPU must process. Additionally, the viewer need only request those portions of the file that correspond to the region of interest; the entire image (at the given level) need not be processed, again saving I/O bandwidth and processing time.
When decompressing the entire image is required, the performance of the decompression step is roughly comparable to that of the earlier compression step: again, MrSID technology is designed to run within reasonable amounts of RAM, even for large datasets. If lossy compression was used, the decompression will be somewhat faster since there is correspondingly less data being read in and processed.
Optimization
For most users, the typical image compression workflow consists of a compression followed by one or more decompressions, either for viewing (small decodes) or for bringing the image back into some other format for some other tool or purpose (large decodes). In many cases, however, the need for the large decode step can be reduced.
Once an image is in the MrSID format, a new MrSID file can be generated from it without resorting to a decode followed by a re-encode - this means you can generate derivative products from a single source. This is referred to as “optimizing” the image.
Optimization allows for creating the following: MrSID files with a lower baseline resolution - for example, resolution levels can be removed if only one foot per pixel resolution is needed from a six-inch resolution image; A MrSID file requiring less storage space - for example, 20:1 compression can be used to fit the image onto a CD or DVD; A MrSID file containing less area - for example, a scene containing only a certain neighborhood can be extracted from an image covering a whole city.
Again, to meet these three different requirements (or perhaps some combination of them) only one fast step is required to generate a new MrSID file from the original MrSID file. There is no need to decode the entire image first.
Metadata
Because MrSID is a geospatial data format, MrSID files also include geospatial referencing information such as the coordinate reference system (CRS), the geographic extents (corner points) of the image, and the pixel resolution. This metadata is an inherent part of the MrSID file format and is based on the well-known GeoTIFF tag scheme. When performing a reprojection operation or one of the optimization steps described above, the metadata is updated to reflect the properties of the derived image: when performing scale reduction, for example, the resolution metadata is updated accordingly. MrSID metadata also is used to record what operations may have been performed on your dataset. For example, you can determine if the file you have still corresponds to the lossless original data or if it has been modified in some way. This native geographic metadata support allows you use a third-party application to import your MrSID imagery for use as a base map with other georeferenced datasets you might have.
Multispectral Support
For many years, some types of geospatial data have included more than just the usual three color (RGB) bands. Only recently, however, have these kinds of multispectral datasets started to be widely available to GIS users. For example, in 2011, USDA’s NAIP program plans to collect data for 15 states which will contain the red, green, and blue (RGB) bands plus a fourth infrared (IR) band. DigitalGlobe’s recently launched WorldView 2 satellite records RGB plus five additional bands: a yellow band, two IR bands, and two “coastal” bands. Other remote sensing platforms are now collecting hyperspectral datasets, typically one hundred or more narrow bands. All these additional bands are chosen for their abilities to improve feature classification and extraction by providing more discriminating information in areas such as vegetation cover, shallow-water bathymetry, and man-made features.
To support these new, richer datasets, the MrSID technology can compress images with up to 255 bands. The same key features are still available: lossless and lossy encoding, multiple resolution levels, and selective decoding. As more data is being encoded and decoded, of course, more time will be required. The time required scales linearly, when normalized to the number of bands. That is, if it takes 1 minute to encode a 1-banded image, it will take 10 minutes to encode an 10-banded image of the same width and height.
The time required to decode imagery with varying numbers of bands scales similarly. However, many users of multispectral imagery only view one or perhaps three of the bands at a time, mapping the bands into the familiar grayscale or RGB space. In the same way that the MrSID algorithms will perform selective decompression for viewing only the scene of interest, they will also decode only the bands of interest.
Differences among the MG2, MG3, and MG4 Formats
As the MrSID technology has evolved over the years, the range of capabilities supported has evolved as well.
Specifically:
- MG2 does not support lossless compression
- MG2 does not support optimization
- MG2 does not support composite images
- Only MG2 supports 32-bit floating point data
- Only MG4 supports signed integer data
- Only MG4 supports alpha masking
- Only MG4 offers support for multispectral and hyperspectral imagery.
While some applications may only write newer versions of the MrSID format, all applications that read MrSID files will always continue to support all versions of the format. These considerations are important to keep in mind, since there are so many older MG2 and MG3 files kept in long-term archives.
IV. MrSID Technology for LiDAR
After what seems like only a few years, LiDAR is now becoming a mainstream GIS technology. LiDAR data is already being used in a variety of areas, including utility corridor monitoring, construction of centimeter-accurate surface and elevation models, and vegetation or biomass measurement.
As with raster imagery, however, this data comes with a cost: file size. A typical day of LiDAR acquisition can result in a dataset hundreds of gigabytes in size and the amount of data collected will continue to grow as sensors improve in resolution and functionality. Large files mean storage hassles and hampered interactive workflows. But technologies like MrSID have been developed to address those problems for raster imagery - can the MrSID technology be used for LiDAR point clouds as well?
LiDAR data is fundamentally different from image data in three ways. First, and most obviously, we have a Z height component in LiDAR data. Second, we may also have a set of attributes associated with each point, such as intensity, classification label, or transmitted time of the laser pulse - more than just the pixel value (color) in images. And third, the LiDAR data do not lie on an implicit regular grid, as image data do: each LiDAR point must be stored explicitly, as we cannot infer position based on an implicit grid location.
Although the algorithms differ, the MrSID compression support for LiDAR gives still the same core features we find in the raster world.
Selective decompression - As the point cloud data is encoded, a spatial index is created which keeps track of where the compressed points are located in geographic space, regardless of where they may be located in the MrSID file. This means that the data for a desired region (bounding box) can be accessed and decoded without reading (or, worse, decoding) the whole file as may be the case with LAS files.
Multiple resolutions - Because the data is on an irregular grid, the multiresolution (pyramid) scheme described earlier for raster imagery is not as effective. Instead, the MrSID file is designed so that applications may request a certain density of points within the region of interest; as further requests are made, additional points may be retrieved. This allows an application to try to achieve a uniform point density across the entire dataset, rather than have an excess of points in some areas when the workflow does not require them.
Lossless and lossy compression - The data points are encoded using, again, techniques similar to the MrSID algorithms for raster compression, allowing for typical lossless compression ratios of 4:1. Lossy compression ratios of 10:1 or higher are typical. However, lossy compression is achieved only by removing some points from the dataset, unlike the approximation technique intuitively described above. (Consider that if the decimal value of a point position was “rounded”, then the point would actually move in space; this is a more significant issue for high-accuracy elevation workflows than for workflows using the intensity values of imagery.)
The time required to read the MG4 file is significantly slower for large scenes (over a third of the file, in this case) due to the computational overhead of the decompression algorithms. For smaller scenes, more realistic of many viewing and analysis workflows, the built-in spatial index inherent in the MG4 format dramatically speeds up the data access compared to LAS.
V. LizardTech’s Products and Integrations
LizardTech was formed as a spin-off from Los Alamos National Laboratory to commercialize their MrSID compression technology. Since its first commercial release in 1998, the MrSID file format has become an industry standard. Today LizardTech offers a number of products that create, manage, and distribute MrSID imagery.
GeoExpress
The GeoExpress application is LizardTech’s flagship product for compressing imagery. It supports creation of MrSID files and includes tools for mosaicking, reprojecting, and color balancing imagery. The latest release, GeoExpress 8, adds support for the MG4 format. GeoExpress also fully supports JPEG 2000, an ISO standard technology similar to MrSID technology.
LiDAR Compressor
The LiDAR Compressor application is LizardTech’s first product to support LiDAR data with the new MG4 format. The software supports lossless compression up to 4:1 and offers both mosaicking and previewing. It supports reading both the LAS and ASCII point cloud file formats.
Express Server
The LizardTech Express Server system is the best solution for distributing MrSID imagery over the internet. A client connected to a website running the Express Server image server can download and view high-resolution imagery quickly using industry-standard protocols such as WMS. Client applications can include browser plug-ins for the desktop, applications on hand-held devices, or enterprise GIS applications.
The Express Server system can also be used in combination with ESRI’s ArcGIS Server and ArcGIS Image Server products to speed up image delivery. You can also publish Express Server catalogs as layers in ArcGIS Server and ArcGIS Image Server, or you can connect an ArcMap client directly to Express Server host so you can work with datasets hundreds of gigabytes in size right on your desktop.
GeoViewer and ExpressView
LizardTech offers two freely downloadable viewers for MrSID imagery. GeoViewer is a standalone application for viewing raster imagery, vector overlays and LiDAR data. With GeoViewer you can combine, view and export visual layers from varied sources, such as local repositories, Express Server catalogs, and WMS servers.
The ExpressView Browser Plug-in enables you to view MrSID imagery in Internet Explorer or Firefox. Like GeoViewer, ExpressView enables you to save a portion of an image in a number of other image formats.
LizardTech MrSID Decode SDK
LizardTech offers an SDK to enable MrSID file format support in third-party applications. The SDK exposes C and C++ APIs that enables developers to open raster and LiDAR MrSID files, read the geospatial metadata, and extract scenes of arbitrary size and scale. The SDK is taken from the same code base LizardTech uses to build its own applications.
Our SDK may be downloaded and integrated into your application for free. Versions of the SDK are available for Windows, Linux, Solaris, and Macintosh.
Third Party Integration
Through our SDK program, hundreds of geospatial applications support the MrSID file format. ESRI’s ArcMap, ERDAS’ Imagine, and Google Earth all support importing MrSID imagery as fully georeferenced raster layers.
VI. Conclusion
LizardTech’s MrSID technology is designed to be the most effective storage solution for geospatial imagery and elevation data on the market. We recognize that the quality of your data can be just as important as the cost of storing and accessing it, and we’ve developed the features of MrSID with that in mind:
- Data quality from lossless to visually lossless to lossy
- Compression ratios from 2:1 to 20:1 and beyond
- Multiple resolutions to obviate manually constructing and managing image pyramids
- Selective decompression for fast access to small scenes in big files
- Support for up to 255 spectral bands
- Support for irregular, 3D data sets like elevation data and point clouds.
All these features are available in LizardTech’s own suite of products and, through our partners, the MG2 and MG3 format is supported in all the other major GIS applications on the market today. Third-party adoption for the MG4 raster and LiDAR has already begun.
Every year, more airborne and satellite sensors are collecting more and more data, with new spectral bands and higher bit depths. Our software was developed to compress two-dimensional image data, and is now supporting three-dimensional elevation data. As we look to the future, we are starting to see some customer needs for compressing even more types of data such as sonar, SAR, and datasets with explicit time dimensions. LizardTech and our MrSID technology will continue to track the needs of our industry to make it easier to store, manage, and distribute geospatial data.
Appendix A. What Does it Mean to Compress an Image? How Compression Works
Using Fewer Bytes: Compression at a practical level is reducing the number of bytes, it takes to communicate the data. We can do this in several ways. As an example, let’s consider an array of 16 numbers representing pixel sample values like those discussed above:
{9 9 9 11 11 11 9 9 9 10 9 9 9 11 11 11}
Alternatively, in an averaging method, we would take pairs of numbers starting at the beginning and average them together resulting in the following array of eight numbers {9 10 11 9 9 9 10 11} because the average of 9 and 9 is 9, the average of 9 and 11 is 10, and the average of 9 and 10 is 9 (rounding down to the nearest integer). If these values described a line, the line produced by this array would approximate that produced by the original, but we’ve reduced the amount of data by a factor o f two.
In a run-length encoding method, we replace runs of identical values with just two numbers, the value itself and a repeat count. Using again our array of 16 numbers, we would get this: {9[3] 11 [3] 9[3] 10[1] 9[3] 11 [3]}. With a resulting array of twelve items, the run-length encoding method here gives us a byte savings of almost a quarter.
Using a third approach, a dictionary method, we remark common sequences of values and replace them with special tokens, storing the sequences and the associated tokens in a dictionary at the top of the file.
Dictionary: A = 9 9 9 B = 11 11 11 Data: A B A 10 A B
Here we’ve reduced the actual data to just six items, but we have to store the dictionary too.
These are very simplistic examples using a short, unrepresentative input, but we can make some observations. First, it might take some time to encode or decode: think about the time involved in searching for and updating those common sequences, for example.
Second, you might lose data: in the “averaging” example we’ve discarded data in the rounding operation and can never get it back. Compressed image files can be described as either lossless or lossy. Lossless means that no pixel data has actually been discarded; even if the number of bits it takes to describe the data has been reduced, you can still reverse the process and arrive at the exact same data that you started with. The run-length encoding and dictionary methods above represent lossless compression. That is, using the run-length duets or the dictionary and six data values, you can reconstruct the original string of 16 numbers. The averaging method, however, is lossy. You can’t infer the 16 original values from the eight averaged values. The precision lost by that encoding process is lost for good.
Appendix B. Compression with MrSID Technology
Adapted from “Compressing Lidar Data”, Michael P. Gerlek, PE&RS, November 2009.
The MrSID technology relies on two key algorithms to encode data. First, a wavelet is used to change the data into a form that serves to represent the data at multiple resolutions. The wavelet transform is a mathematical transformation of the data that is, in general, lossless. The second step is to encode the data produced by the wavelet transform into a new representation that is significantly more compact than the original and yet still lossless; optionally, this step may also reduce the precision of the data for even more space savings at the cost of incurring some data loss.
Wavelet Encoding
Wavelet encoding can be thought of as nothing more than a weighted averaging and differencing scheme. Consider a list of 4 numbers: {2, 6, 14, 6}. By pairwise averaging, we can reduce this to a “second level” list of two numbers, {4, 10}, and a list of second level “differences”, {+2, -4}. Performing the same operation again on the {4, 10} list, we get the third-level list {7} and the third level difference list {+3}.
These three lists, and the two associated difference lists, are used to represent the original four-element list at three levels of resolution. Observe that only the final
singleton list {7} and two difference lists of {+3} and {+2, -4} are required to perform the inverse operation and restore the original input list. With only these three lists, we can reconstruct the second level: the third level list {7} and the difference list {+3} yields {4, 10} (because 7-3=4 and 7+3=10). The second level list {4, 10} and the second level difference list {+2,-4} yields in turn the original list (4-2, 4+2, 10-(-4), 10+(-4)).
Although the details are somewhat more complicated in practice, the principle is the same for image data. Using a 1D wavelet across both dimensions of the 2D array of pixel data, we reduce the image to a pyramid of images, each level being half the width and height of the previous level and including the corresponding difference list. This is a mathematically lossless process. No significant compression has been achieved, but we have a better representation of the data because it inherently reflects the data at multiple resolution levels. This is similar to the well-known manual image pyramid scheme, which has power-of-two sequential reductions in resolution. These reduced resolution decodes fall directly out of the wavelet decomposition, making them easily accessible.
In the case of LiDAR data, the situation is somewhat different because raster datasets are regularly gridded while point cloud datasets are not. In the former case, we don’t need to explicitly encode the x and y coordinates, just the (pixel) values at each grid point. In the latter case, having no implicit reference grid, we must encode the coordinates and any associated values (such as intensity). In a decompression at less than the full resolution of the data, a subset of the pyramid levels are used to compute the data to be returned; the resulting point cloud is effectively subsampled.
Putting It Together
The wavelet transform followed by the bit plane encoding gives us a representation of the data in the file format that offers some of the capabilities we have discussed in this white paper. For example, a MrSID file can be further compressed (optimized) by simply considering each already-encoded bit plane and truncating its precision by the degree necessary to achieve the smaller target file size. Selective decompression can be achieved by selecting only those blocks of bits relevant to the scene (and resolution scale) and then performing the inverse of the bit plane encoding and the wavelet transform on them. As long as no bit planes have been truncated (incurring data loss), these inverse transforms are numerically lossless, thus ensuring you will get back exactly the original data you started with.
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Ryan Burley LizardTech
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