## 3 Self-Similarity and Multifractal Analysis of Compressed Video Content  
Video can be manipulated in many ways, affecting and controlling the overall quality. The most frequent choices are setting constant quality factor or buffer size or using constant, constrained or variable bit rates [33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. A large number of physical systems and nonstationary signals tend to show similar behavior at different scales, known as having self-similarity properties [34; 35; 36]. These properties have been analyzed using fractal and multifractal theory for compressed video content and video tracing.  
In order to ensure a desirable quality of service, self-similarity is investigated for constant and variable bit rates in [37]. Self-similar patterns are explored for high-speed network traffic in [38]. In early works, long-range dependency or LRD in video traffic represented by traces has been mostly quantified by a single-parameter Hurst exponent [37; 38]. LRD means that traces exhibit correlation over a range of time scales, where among standard statistical video traffic metrics, like mean and variation in video traces, additional self-similarity properties have been investigated under different conditions, where LRD is only one feature of fractal-like behavior. In [39], Transport Control Protocol (TCP) traffic collected through a number of bytes arriving per time is multifractal and is analyzed using spectra, enabling valuable statistical estimation. Multifractals are applied for behavior of a queuing system in [40]. Tail distributions in a multifractal sense while measuring variable bit rate are compared in [41].  
Generally, there are two main directions in analysis of video traces. The first one is traffic modeling. Self-similarity has been widely recognized, and multifractal-based traffic modeling has been found suitable for video tracing [39; 40; 41; 42; 43; 44; 45]. Different self-similarity models are tested for network traffic analysis and prediction: using fractional traffic Brownian motion model [41], wavelets [42; 43], multiplicative approaches [44; 45], autoregressive models [46; 47; 48; 49] and Markov chains [50; 51]. Experimental multifractal analysis is applied for dimensioning, buffer capacity interpretation and statistical multiplexing of video streams [52], as well as for dynamic bandwidth allocation [53]. Multifractal spectra have been compared during the normal work and force attacks in a communication network [54], while differentiation between spectra is used to show the consistency of LRD [55].  
The second direction in investigating self-similarity properties of video traces is oriented towards the characterization of compressed video, having in mind specific standards. Most of the research uses MPEG-4 traces for testing, being one of the most valuable practical standards, like in [56; 57]. MPEG-4 Advanced Simple Profile (ASP)-based encoded traffic is tested for estimating queuing performance [56]. In [57], MPEG-4 version 2 and H.263 video traces are compared using accompanied parsers in order to extract ten sequences, so-called frame size traces, which are found statistically valuable for testing performance. This work has been continued on new encoders like H.264/MPEG-4 AVC [58; 59]. H.264 video compressed traces are analyzed using multifractal and fractal approaches [58]. Trace analysis with extended encoding standards is performed in [59]. The whole encoding or transcoding process takes time and, due to settings, it is hard to compare the former generated traces with the new traces [56; 58]. Frame size trace sequence according to each standard is different.