A Stochastic Model for Video and its Information Rates

Abstract

We propose a stochastic model for video and compute its information rates. The model has two sources of information representing ensembles of camera motion and visual scene data (i.e. "realities"). The sources of information are combined generating a vector process that we study in detail. Both lossless and lossy information rates are derived. The model is further extended to account for realities that change over time. We derive bounds on the lossless and lossy information rates for this dynamic reality model, stating conditions under which the bounds are tight. Experiments with synthetic sources suggest that in the presence of scene motion, simple hybrid coding using motion estimation with DPCM can be suboptimal relative to the true rate-distortion bound.

On the Information Rates of the Plenoptic Function

“…Fig. 3 illustrates 1 Note that when L is even, then we cannot assert that PrfW = 1 j (v ; v ) 2 A g = p .…”

“…Denote by the set of is such that cannot be inferred with probability one. Then, because is odd, it is straightforward to infer that 1 and . Consequently, we have that (17) The set is contained in the set .…”

“…Denote by A 1 the set of (v 1 , v 0 ) is such that W 1 cannot be inferred with with probability one. Then, because L is odd, it is straightforward to infer that 1 Pr…”

Application of 3D-wavelet statistics to video analysis

“…Statistical analysis is one of the basic approaches to temporal modeling [25][26][27][28][29][30]. In [25], a layered Hidden Markov Model (HMM) is introduced to do video semantic analysis.…”

“…In [27] a hidden Markov tree is employed to model relationships between coefficients in 2D wavelet transform. Markov fields are also used in scene modeling [28]. The model combines the visual information and camera motion data and employs the resulting vector to investigate the changes over time and studies lossy and lossless information rates based on the achieved dynamic model and find conditions for tight bounds.…”