1 Compression Ratio
MPEG-i, MPEG-2, MPEG-iv, and H.264
Digital Video and DSP, 2008
MPEG vs. JPEG
JPEG (ISO/IEC 10918-Joint Photographic Experts Group) is an image compression standard that was designed primarily for still images and single video frames. Information technology doesn’t handle bi-level (black and white) images efficiently, and pseudo-color images have to be expanded into the unmapped color representation prior to processing. JPEG images may be of any resolution and color space, with both lossy and lossless algorithms available. If y’all run JPEG fast enough, yous can compress motion video. This is called movement JPEG, or M-JPEG.
Since JPEG is such a general-purpose standard, it has many features and capabilities. By adjusting the diverse parameters, compressed paradigm size tin exist traded against reconstructed image quality over a wide range. Image quality ranges from “browsing” (100:one compression ratio) to “indistinguishable from the source” (about 3:1 pinch ratio). Typically, the threshold of visible difference between the source and reconstructed images is somewhere betwixt a 10:one to 20:1 compression ratio.
How Information technology Works
JPEG does not use a unmarried algorithm, merely rather a family of four, each designed for a certain application. The virtually familiar lossy algorithm is
sequential DCT. Either Huffman encoding (baseline JPEG) or arithmetics encoding may be used. When the prototype is decoded, it is decoded left-to-right, top-to-bottom.
is another lossy algorithm, requiring multiple scans of the image. When the paradigm is decoded, a coarse approximation of the total prototype is available correct away, with the quality progressively improving until consummate. This makes information technology ideal for applications such as image database browsing. Either spectral selection, successive approximation, or both may exist used. The spectral selection option encodes the lower-frequency DCT coefficients first (to obtain an image quickly), followed by the college-frequency ones (to add more than particular). The successive approximation option encodes the more significant bits of the DCT coefficients first, followed by the less pregnant bits.
The hierarchical way represents an image at multiple resolutions. For example, in that location could exist 512×512,×1024×1024, and 2048×2048 versions of the epitome. Higher-resolution images are coded as differences from the next smaller paradigm, requiring fewer bits than they would if stored independently. Of course, the full number of bits is greater than that needed to store just the highest-resolution image. Notation that the private images in a hierarchical sequence may be coded progressively if desired.
As well supported is a lossless spatial algorithm that operates in the pixel domain as opposed to the transform domain. A prediction is fabricated of a sample value using upward to three neighboring samples. This prediction then is subtracted from the bodily value and the difference is losslessly coded using either Huffman or arithmetic coding. Lossless performance achieves about a 2:one pinch ratio.
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Railway Applied science
Encyclopedia of Physical Science and Technology (Third Edition), 2003
Diesel fuel Engine
The prime number mover for a diesel-electric locomotive is a pinch-fired internal combustion engine. The four-stroke engine uses separate strokes for intake of fuel, compression (and ignition), power delivery, and exhaust or scavenging. The 2-bicycle engine combines intake and compression in one stroke and power delivery and exhaust in the 2d stroke. A mod 16-cylinder engine having a ten- to 11-in. stroke will have a cylinder displacement of 600–700
with a 16:1 compression ratio.
The heart of the engine is the injector gear up in the caput of the cylinder. A constant-stroke plunger pump operating from a camshaft delivers fuel to the cylinders in a measured atomized spray (about 0.03
oz) forced through the injector tips at xv,000–20,000
psi force per unit area. Efforts to ameliorate fuel efficiency through estimator control of speed, adjusting it to the load, and use of organic-based petroleum additives take effected a v–xiv% increment in fuel efficiency in contempo models.
Ignition occurs at a pressure of about 600
psi and a temperature of g
°F. A fine clearance of about 0.000025
in., a big amount of air, and rugged construction are required of the injector. Additional air is obtained at loftier altitudes from a multibladed compressor or supercharger. The throttle that controls fuel admission and engine speed usually has eight settings or “notches.” The 8th notch represents total engine output at engine speeds of 500–3000
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Multimedia Networks and Communication
The Electric Engineering Handbook, 2005
Graphics and Animation
Graphics and blitheness include static media types like digital images and dynamic media types like wink presentations. An uncompressed, digitally encoded image consists of an array of pixels, with each pixel encoded in a number of bits to stand for luminance and color. Compared to text or digital sound, digital images tend to exist big in size. For instance, a typical 4 × 6 inch digital image, with a spatial resolution of 480 x 640 pixels and colour resolution of 24 bits requires ∼ 1 MB of storage. To transmit this paradigm on a 56.vi Kbps line will take at least ii min. If the image is compressed at the small-scale 10:1 pinch ratio, the storage is reduced to ∼ 100 KB, and transmission time drops to ∼ 14 sec. Thus, some course of compression schemes is always used that cashes on the property of loftier spatial redundancy in digital images. Some popular compression schemes (
Salomon, 1998) are illustrated in
Table vii.3. Virtually modern paradigm compression schemes are progressive and have important implications for transmission over the communication networks (Kisner, 2002). When such an image is received and decompressed, the receiver tin display the image in a low-quality format and then improve the display as subsequent paradigm information is received and decompressed. A user watching the image display on the screen can recognize near of the image features after only v to x% of the information has been decompressed. Progressive compression can be achieved by: (1) encoding spatial frequency data progressively, (2) using vector quantization that starts with a greyness image and later adds colors to information technology, and (3) using pyramid coding that encodes images into layers, in which early layers are low resolution and later layers progressively increase the resolution.
Tabular array 7.iii.
Paradigm Compression Schemes
|Graphics interchange format (GIF)||GIF supports a maximum of 256 colors and is all-time used on images with sharply defined edges and big, flat areas of color similar text and line-based drawings. GIF uses LZW compression to make files small. This is a lossless compression scheme.|
|Portable network graphics (PNG)||PNG supports whatsoever number of colors and works all-time with most any type of image. PNG uses the zlib compression scheme, compressing information in blocks dependent on the “filter” of choice (usually
This is a lossless pinch scheme and does non back up animation.
|Joint photographic experts group (JPEG)||JPEG is best suited for images with subtle and smoothen color transitions, such as photographs gray-calibration, and colored images. This pinch standard is based on the Huffman and run-length encoding of the quantized detached cosine transform (DCT) coefficients of image blocks. JPEG is a lossy compression. Standard JPEG encoding does not allow interlacing, but the progressive JPEG format does. Progressive JPEGs start out with large blocks of color that gradually get more detailed.|
|JPEG 2000||JPEG 2000 is suitable for a wide range of images, from those produced by portable digital cameras to advanced prepress and medical imaging. JPEG 2000 is a new image coding system that uses state-of-the-fine art pinch techniques based on wavelet engineering that stores its information in a data stream instead of blocks as in JPEG. This is a scalable lossy compression scheme.|
|JPEG-LS||JPEG-LS is suitable for continuous-tone images. The standard is based on the LOCO-I algorithm (Low Complexity LOssless COmpression for images) developed by HP. This is a lossless/near-lossless compression standard.|
|Joint bilevel image experts group (JBIG)||JBIG is suitable for compressing black-and-white monochromatic images. It uses multiple arithmetic coding schemes to shrink the paradigm. This is a lossless type of compression.|
Images are fault tolerant and can sustain packet loss, provided the application used to render them knows how to handle lost packets. Moreover, images, similar text files, do not have any real-time constraints.
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MPEG-1 and -2 Compression
Multimedia Communications, 2001
THE MPEG MODEL
A primal to understanding MPEG is agreement both the bug that MPEG set out to accost in developing MPEG-1 and -2 (although it is probable MPEG will be applied in many unanticipated places too) and the fundamental models that underlie the algorithms and that are used to foster interoperability.
Key Applications and Problems
Some of the about of import applications to bulldoze the development of MPEG include disk-storage-based multimedia, broadcast of digital video, switched digital video, high-definition tv, and networked multimedia.
MPEG-1 had its genesis as the solution to a very specific compression problem: how to best compress an audio-video source to fit into the data rate of a medium (CD-ROM) originally designed to handle uncompressed audio lone. At the time MPEG started, this was considered a hard goal. Using an uncompressed video rate for 8-bit active video samples [Comité Consultatif International des Radiocommunications or International Telecommunications Marriage—Radio (CCIR)-601 chroma sampling)] of approximately 210 Mbit/s, this requires a rather aggressive 200:1 pinch ratio
to achieve the slightly greater than i Mbit/s or so bachelor subsequently forrad fault correction and compressed sound on a typical CD-ROM.
Aside from the substantial pinch requirement, another requirement of many videos on CD-ROM applications is a reasonable random access adequacy, that is, the ability to start displaying compressed material at any point in a sequence with predictable and minor filibuster. This is a fundamental attribute, for instance, of many interactive game and training materials.
More recently, a new optical disk format with much higher capacity than CD-ROM has been adult. Called digital versatile disc (DVD) (renamed from the original “digital video disc” to include information-storage applications), its college rates, combined with the apply of variable-rate encoding, can provide video quality that surpasses that currently available to consumers through other video media [(e.g., Video Dwelling Organization (VHS) tape, laserdisc, cable and off-air analog television], also every bit cinematic audio and a number of unique admission and format features.
Strategy for Standardization
A cardinal purpose of a standard is to facilitate interoperability. A good standard achieves this while maximizing back up for current and as-yet-unknown applications and the evolution of a variety of implementations. For MPEG, this is accomplished past focusing standardization on two related questions:
What is a legal MPEG bit stream?
What should be done with information technology to generate displayable sound-video material?
The first question is answered by a careful specification of the legal syntax of an MPEG chip stream, that is, rules that must be followed in amalgam a bit stream. The second is answered by explaining how an idealized decoder would process a legal bit stream to produce decoded audio and video.
This particular strategy for standardization allows a great deal of breadth in the design of encoding systems because the range betwixt truly efficient bit streams (in terms of quality preserved versus bits spent) and inefficient just legal bit streams can be big. At that place is less latitude in decoder design, since the decoder must not deviate from the arcadian decoder in terms of the bit streams it tin can procedure, but there is still room for different and clever implementations designed to reduce cost in specific applications, improve robustness to slightly damaged bit streams, and provide different levels of quality in post-MPEG processing designed to set up a signal for display (e.1000., interpolation, digital-to-analog conversion, and blended modulation).
The bodily details of what constitutes a legal bit stream are largely conveyed through the specification of the syntax and semantics of such a bit stream.
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MPEG-4, H.264/AVC, and MPEG-vii: New Standards for the Digital Video Industry
Handbook of Image and Video Processing (Second Edition), 2005
MPEG-iv Compression Performance
In this department, nosotros first present experimental results that compare the coding performance of frame-based coding to object-based coding using an MPEG-4 Part 2 codec on some progressive-scan video content. Next, the coding efficiency of H.264/AVC is compared to that of the prior standards.
MPEG-four Part 2
While MPEG-4 Part 2 as well yields significantly improved coding efficiency over the previous coding standards
(e.g., 20-30% scrap rate savings over MPEG-2 ), its main advantage is its object-based representation, which enables many desired functionalities and can yield substantial savings in bit rate savings for some low-complication video sequences. Here, we present an example that illustrates such a coding efficiency advantage.
The simulations were performed past encoding the colour sequence
at CIF resolution (352 × 288 luma samples/frame) at 10 frames per 2d (fps) using a constant quantization parameter of 10. The sequence shows a moderate motility scene with a fish swimming and changing directions. We used the MPEG-iv Part ii reference codec for encoding. The video sequence was coded (a) in frame-based mode (b) in object-based mode at 10 fps. In the frame-based mode, the codec accomplished a 56:1 compression ratio
with relatively high reconstruction quality (34.4 dB). If the quantizer footstep size were larger, it would exist possible to achieve up to a 200:1 compression ratio for this sequence, while nonetheless keeping the reconstruction quality above 30 dB. In the object-based mode, where the background and foreground (
fish) objects are encoded separately, a pinch ratio of eighty:1 is obtained. Since the background object did not vary with time, the number of bits spent for its representation was very small. Hither, it is as well possible to employ sprite coding by encoding the background as a static sprite.
The peak signal-to-noise ratio (PSNR) versus rate operation of the frame-based and object-based coders for the video sequence
is presented in
Fig. xx. Equally shown in the figure, for this sequence, the PSNR-chip rate tradeoffs of object-based coding are amend than those of frame-based coding. This is mainly due to the constant background, which is coded but one time in the object-based coding example. All the same, for scenes with complex and fast varying shapes, since a considerable amount of bits would be spent for shape coding, frame-based coding would achieve meliorate pinch levels, but at the cost of a limited object-based admission adequacy.
MPEG-4 Part 10: H.264/AVC
Adjacent, the coding performance of H.264/AVC is compared with that of MPEG-ii, H.263 and MPEG-4 Part two. The results were generated using encoders for each standard that were similarly optimized for rate-baloney operation using Lagrangian coder control. The use of the same efficient charge per unit-distortion optimization method, which is described in , allows for a fair comparing of encoders that are compliant with the respective standards. Here, we provide one set of results comparison the standards in 2 cardinal application areas: depression-latency video communications and amusement-quality broadband video.
In the video communications test, we compare the charge per unit-baloney performance of an H.263
encoder, which is the near widely deployed conformance point for such applications, with an MPEG-4 unproblematic profile encoder and an H.264/AVC baseline profile encoder. The rate-distortion curves generated by encoding the color sequence
at CIF resolution (352 × 288 luma samples/frame) at a rate of 15 fps are shown in
Fig. 21. As shown in the figure, the H.264/AVC encoder provides significant improvements in coding efficiency. More specifically, H.264/AVC coding yields fleck rate savings of approximately 55% over H.263 baseline profile and approximately 35% over MPEG-4 Part two simple contour.
A 2nd comparison addresses broadband entertainment-quality applications, where college resolution content is encoded and larger amounts of latency are tolerated. In this comparison, the H.264/AVC main profile is compared with the widely implemented MPEG-two chief profile. Rate-baloney curves for the interlaced sequence
(720 × 576) are given in
Fig. 22. In this plot, nosotros tin can see that H.264/AVC tin yield similar levels of objective quality at approximately half the chip rate for this sequence. In addition to these objective rate-baloney results, extensive subjective testing conducted for the MPEG verification tests of H.264/AVC have
confirmed that like subjective quality can be achieved with H.264/AVC at approximately half the bit rate of MPEG-2 encoding .
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Comprehensive Microsystems, 2008
One distinctive characteristic of a gas micropump is the maximum force per unit area differential or the maximum dorsum force per unit area information technology can produce.
illustrates a typical performance curve of a gas pump, which shows that the pressure differential created by the pump decreases every bit the pump menses rate is increased. The maximum back pressure is the pressure at which the pump flow rate is zero. Information technology indicates the maximum pressure that the micropump can work against while fugitive negative period rates.
In a gas micropump, thermodynamic considerations bear witness that the maximum pressure differential is determined past the compression ratio (CR) of the pump, every bit described in
. Hither the compression ratio is defined as the modify in volume divided by the original volume of the pumping chamber
is the maximum dorsum force per unit area,
is the absolute inlet pressure level, ΔV
is the volume change of the pumping chamber, and
is the pumping cavity volume. Hither isothermal compression is assumed. For example, if the pump is compressed by xx% of its original volume, the pressure inside the chamber increases by 20%. Thus, a high pressure differential tin exist achieved by obtaining a loftier compression ratio, which could result from either by straight compressing the gas by moving a pumping membrane or by expanding the volume of the gas thermally in the pumping cavity. The pump by
employs a flexible polyimide membrane to create a big deflection to compress the pumping chamber with a high compression ratio, whereas the pump reported past
produces merely a small pressure level differential of 2
kPa because it transfers gas without compression cycles. Other researchers have taken reward of the high thermal expansion of gas to achieve college effective pinch ratio than typical diaphragm pumps (McNamara and Gianchandani 2005, Vargo
1999, Young 1999). In practice, the pinch ratio is lower than predicted by theory due to imperfect valves and leakage.
Pressure differential can be accumulated using multiple pumping chambers connected in serial, each with a certain compression ratio.
shows the increment in pressure when multiple pumping chambers are used. If the compression ratio is large (CR
0.5), the pressure differential in the final few stages is much larger than that in the get-go few stages. All the same, when the pinch ratio is small-scale (CR
0.02), the differential pressures across all the stages are approximately equal (Astle
2002, 2007). This feature of the multiple-chamber configuration is very attractive for MEMS micropumps because it allows to distribute the required pumping actuation strength uniformly across many pumping chambers. A high overall pressure level differential tin can be achieved while limiting the compression ratio and the force per unit area differential for each stage. For example, Kim
cascaded several micropumps and reported the first functional peristaltic configuration achieving a high force per unit area differential (>17
kPa) for the whole pump. The pinch ratio for each stage in this pump was less than five% (Kim
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Subband and Wavelet-Based Coding
Digital Bespeak Processing (Third Edition), 2019
Wavelet Transform Coding of Signals
Nosotros can apply the DWT and IWDT for data pinch and decompression. The compression and decompression involves two stages, that is, the analysis stage and the synthesis stage. At analysis stage, the wavelet coefficients are quantized based on their significance. Usually, we assign more than bits to the coefficient in a coarser scale, since the corresponding subband has larger signal free energy and low-frequency components. We assign a small number of bits to the coefficient, which resides in a finer scale, since the corresponding subband has lower signal energy and high-frequency components. The quantized coefficients can be efficiently transmitted. The DWT coefficients are laid out in a format described in
Fig. 12.41. The coarse coefficients are placed toward the left side. For example, in
Example 12.7, we organized the DWT coefficient vector every bit
Permit us look at the following simulation examples.
Given a 40-Hz sinusoidal betoken plus random noise sampled at 8000
Hz with 1024 samples,
is a random racket generator with a unit ability and Gaussian distribution. Use a 16-scrap code for each wavelet coefficient and write a MATLAB programme to perform data compressions for each of the following ratios: 2:1, four:one, 8:1, and xvi:ane. Plot the reconstructed waveforms.
We apply the viii-tap Daubechies filter every bit listed in
. We achieve the data compression by dropping the loftier subband coefficients for each level consecutively and coding each wavelet coefficient in the lower subband using sixteen bits. For example, nosotros achieve the 2:one compression ratio
past omitting 512 loftier-frequency coefficients at the start level, 4:1 by omitting 512 high-frequency coefficients at first level and 256 loftier-frequency coefficients at the second level, so on. The recovered signals are plotted in
Fig. 12.42. SNR =
dB is accomplished for the 2:1 compression ratio. As we tin can see, when more and more higher frequency coefficients are dropped, the reconstructed signal contains less and less details. The recovered signal with the compression of sixteen:one presents the least details but shows the smoothest signal. On the other hand, omitting the high-frequency wavelet coefficients tin can be very useful for a signal denoising application, in which the loftier-frequency noise contaminating the clean point is removed. A complete MATLAB program is given in Programme 12.ii.
Program 12.ii. Wavelet data compression.
circular(2ˆ15⁎west/wmax); % 16-scrap code for storage
wcode⁎wmax/2ˆ15; % Recovered wavelet coefficients
zeros(1512); % ii:1 pinch ratio
0; % 4:one pinch ratio
0; % 8:ane pinch ratio
0; % sixteen:1 compression ratio
subplot(5,1,1),plot(t,x,’thou’); centrality([0 0.12–120,120]);ylabel(‘ten(north)’);
subplot(5,1,2),plot(t,rec_sig2t1,’k’); axis([0 0.12–120,120]);ylabel(‘2:1’);
subplot(5,i,3),plot(t,rec_sig4t1,’k’); centrality([0 0.12–120,120]);ylabel(4:ane);
subplot(five,1,4),plot(t,rec_sig8t1,’thou’); axis([0 0.12–120,120]);ylabel(‘8:1’);
subplot(5,1,5),plot(t,rec_sig16t1,’k’); axis([0 0.12–120,120]);ylabel(’16:1′);
min(length(x),length(rec_sig2t1)); axis([0 0.12–120,120]);
disp(‘PR reconstruction SNR dB
shows the wavelet compression for 16-chip speech data sampled at 8
kHz. The original speech data is divided into speech segments, each with 1024 samples. After applying the DWT to each segment, the coefficients, which correspond to loftier frequency components indexed from 513 to 1024, are discarded in order to achieve the coding efficiency. The reconstructed spoken language information has a compression ratio 2:1 with SNR
dB. The MATLAB program is given in Program 12.3.
Program 12.iii. Wavelet data pinch for oral communication segments.
load orig.dat; %Load spoken language data
orig(ane:North);% Making the spoken language length to be multiple of 1024 samples
zeros(1512); % Omitting the high frequency coefficients
subplot(2,one,i),plot([0:length(speech)-1],speech,’1000′);axis([0 20,000–20,000 20,000]);
ylabel(‘Original data x(n)’);
subplot(2,one,2),plot([0:length(rec_sig)-1],rec_sig,’thou’);axis([0 20,000–twenty,000 20,000]);
xlabel(‘Sample number’);ylabel(‘Recovered 10(n) CR
disp(‘PR reconstruction SNR dB
displays the wavelet compression for 16-bit ECG data using Program 12.3. The reconstructed ECG data has a compression ratio of 2:1 with SNR
illustrates an application of signal denoising using the DWT with coefficient threshold. During the assay stage, the obtained DWT coefficient (quantization is not necessary) is ready to zero if its value is less than the predefined threshold every bit depicted in
Fig. 12.45. This simple technique is chosen the hard threshold. Usually, the small wavelet coefficients are related to the high-frequency components in signals. Therefore, setting loftier-frequency components to zip is the aforementioned as lowpass filtering.
An example is shown in
Fig. 12.46. The starting time plot depicts a 40-Hz noisy sinusoidal signal (sine wave plus racket with SNR
dB) and the clean signal with a sampling rate of 8000
Hz. The second plot shows that after zero threshold operations, 67% of coefficients are set to zero and the recovered signal has a SNR
dB. Similarly, the third and 4th plots illustrate that 93% and 97% of coefficients are gear up to nil after threshold operations and the recovered signals accept the SNR
23 and 28
dB, respectively. As an evidence that the point is smoothed, that is, the loftier frequency noise is attenuated, the wavelet denoise technique is equivalent to lowpass filtering.
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3D Mesh Compression
Visualization Handbook, 2005
 has potent similarities to Edgebreaker. Considering it requires the explicit encoding of the offset of Southward triangles and because it was designed to support manifold meshes with boundaries, the cut-border method is slightly less effective than Edgebreaker. Reported connectivity pinch results range from one.viit
bits. A context-based arithmetics coder farther improves them to 0.95t $.25 . Gumhold [xvi] proposes a custom variable-length scheme that guarantees less than 0.94t
bits for encoding the offsets, thus proving that the cutting-border car has linear complexity.
Turan  noted that the connectivity of a planar triangle graph tin can be recovered from the structure of its VST and TST, which he proposed to encode using a total of roughly 125
bits. Rossignac  has reduced this total cost to viv
bits by combining ii observations: (ane) The binary TST may exist encoded with 2t
bits using ane fleck per triangle to betoken whether it has a left child and another one to indicate whether it has a right kid. (2) The respective (dual) VST may exist encoded with anet
bit per vertex indicating whether the node is a foliage and the other bit per vertex indicating whether information technology is the concluding child of its parent. (Remember that 2five
+ 4.) This scheme does not impose any brake on the TST. Annotation that for less than the 2t-$.25 budget needed for encoding the TST alone, Edgebreaker  encodes the
string, which describes non just how to reconstruct the TST, just also how to orient the borders of the resulting web so as to define the VST and hence the consummate incidence. This surprising efficiency seems linked to the restriction of using a
Taubin and Rossignac have noticed that a spiraling VST, formed past linking concentric loops into a tree, has relatively few branches. Furthermore, the corresponding dual TST, which happens to be identical to the TST produced past Edgebreaker, also by and large has few branches (Fig. xviii.vii). They have exploited this regularity by
Run Length Encoding
(RLE) the TST and the VST. Each run is formed by sequent nodes that have a single child. The resulting
3D pinch technique [61,
62] encodes the length of each run, the structure of the copse of runs, and a marching pattern, which encodes each triangle run every bit a generalized
[ten] using i bit per triangle to indicate whether the next triangle of the run is attached to the right or to the left border of the previous i. An IBM implementation of the topological surgery compression has been developed for the VRML standard  for the manual of 3D models across the Internet, thus providing a compressed binary alternative to the original VRML ASCII format [71
], resulting in a 50-to-1 pinch ratio. Subsequently, the topological surgery approach has been selected as the core of the Iii-Dimensional Mesh Coding (3DMC) algorithm in MPEG-4 [
38], which is the ISO/IEC multimedia standard adult by the Moving Film Experts Group for digital television, interactive graphics, and interactive multimedia applications.
Instead of linking the concentric rings of triangles into a unmarried TST, the
color coded in
(left) may be preserved . The incidence is represented by the total number of vertex layers, and past the triangulation of each layer. When the layer is elementary, its triangulation may be encoded as a
triangle strip, using 1 marching chip per triangle, as was originally done in the topological surgery approach. However, in do, a significant number of overhead bits is needed to encode the connectivity of more than complex layers. The topological surgery approach resulted from an attempt to reduce this boosted cost past chaining the consecutive layers into a single TST (run across
Focusing on hardware decompression, Deering  encodes generalized triangle strips using a buffer of 16 vertices. I bit identifies whether the next triangle is attached to the left or the right border border of the previous triangle. Another bit indicates whether the tip of the new triangle is encoded in the stream or is still in the buffer and can hence be identified with but 4 $.25. Boosted $.25 are used to manage the buffer and to indicate when a new triangle strip must be started. This compressed format is supported by Coffee 3D’s Compressed Object node . Chow [v] has provided an algorithm for compressing a mesh into Deering’s format by extending the edge of the previously visited part of the mesh by a fan of non-even so-visited triangles effectually a border vertex. When the tip of the new triangle is a previously decoded vertex no longer in the cache, its coordinates, or an absolute or relative reference to them, must be included in the vertex stream, significantly increasing the overall manual price. Therefore, the optimal encoding traverses a TST that is different from the spiraling TST of Edgebreaker in an endeavour to reduce cache misses.
Given that there are 3 corners per triangle and that
– 4, at that place are roughly 6 times as many corners equally vertices. Thus, the
average valence, i.eastward., the number of triangles incident upon a vertex, is 6. In nigh models, the valence distribution is highly full-bodied around half dozen. For example, in a subdivision mesh, all vertices
that do not correspond to vertices of the original mesh have valence 6. To exploit this statistic, Touma and Gotsman  have developed a valance-based encoding of the connectivity, which visits the triangles in the same order as Edgebreaker does. Every bit in Edgebreaker, they encode the distinction betwixt the C and the South triangles. However, instead of encoding the symbols for L, R, and East, they encode the valence of each vertex and the starting time for each S triangle. When the number of incident triangles around a vertex is one less than its valence, the missing 50, R, or E triangle may exist completed automatically. For this scheme to piece of work, the start must encode not but the number of vertices separating the gate from the tip of the new triangle along the edge (Fig. 18.2), just also the number of triangles incident on the tip of the S triangle that are part of the right hole. To better capeesh the power of this approach, consider the statistics of a typical case. Just one scrap is needed to distinguish a C from an Due south. Given that l% of the triangles are of type C and nigh five% of the triangles are of type Southward, the amortized entropy cost of that bit is around 0.22t
bits. Therefore, about eighty% of the encoding price lies in the valence, which has a low entropy for regular and finely tessellated meshes and in the encoding of the offsets. For case, when lxxx% of the vertices have valence six, a bit used to distinguish them from the other vertices has entropy 0.72 and hence the sequence of these $.25 may be encoded using shut to 0.36t
bits. The amortized price of encoding the valence of the other 20% vertices with 2 bits each is 0.40t
bits. Thus, the valence of all vertices in a reasonably regular mesh may be encoded with 0.76t
bits. If v% of the triangles are of blazon S and each starting time is encoded with an average of 5 $.25, the amortized cost of the offsets reaches
$.25. Note that the offsets add well-nigh 25% to the price of encoding the C/S bits and the valence, yielding a total of 1.23t
bits. This price drops downward significantly for meshes with a much higher proportion of valence-half-dozen vertices.
Although attempts to combine the Edgebreaker solution that avoids sending the offsets with the valence-based encoding of the connectivity have failed, Alliez and Desbrun  managed to significantly reduce the total cost of encoding the offsets by reducing the number of Southward triangles. They apply a heuristic that selects as gate a border edge incident upon a border vertex with the maximal number of incident triangles. To further compress the offsets, they sort the border vertices in the agile loop according to their Euclidean distances from the gate and encode the offset values using an arithmetics range encoder . They as well show that if 1 could eliminate the S triangles, the valence-based arroyo would guarantee pinch of the mesh with less than 1.62t
bits, which happens to exist
Tutte’s lower bound
An improved Edgebreaker compression arroyo was proposed [56,
57] for sufficiently large and regular meshes. Information technology is based on a specifically designed context-based coding of the
string and uses the Spirale Reversi decompression. For a sufficiently big ratio of degree-six vertices and a sufficiently large
t, this approach is proven to guarantee a worst-case storage of 0.81t
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