Coding B-Frames of Color Videos with Fuzzy Transforms

We use a new method based on discrete fuzzy transforms for coding/decoding frames of color videos in which we determine dynamically the GOP sequences. Frames can be differentiated into intraframes, predictive frames, and bidirectional frames, and we consider particular frames, called Δ-frames (resp., R-frames), for coding P-frames (resp., B-frames) by using two similarity measures based on Lukasiewicz -norm; moreover, a preprocessing phase is proposed to determine similarity thresholds for classifying the above types of frame. The proposed method provides acceptable results in terms of quality of the reconstructed videos to a certain extent if compared with classical-based F-transforms method and the standard MPEG-4. 1. Introduction A video can be considered as a sequence of frames of sizes ; a frame is an image that can be compressed by using a lossy compression method. We can classify each frame as intraframe (for short, I-frame), predictive frame (for short, P-frame), and bidirectional frame (for short, B-frame) which is more compressible than I-frame. A B-frame can be predicted or interpolated from an earlier and/or later frame. In order to avoid a growing propagation error, a B-frame is not used as a reference to make further predictions in most encoding standards except in AVC [1]. A frame can be considered as a P-frame if it is “similar” to the previous I-frame in the frame sequence; otherwise, it must be considered as a new I-frame. This similarity relation between a P-frame and the previous I-frame is fundamental in video-compression processes because a P-frame has values in its pixels very close to the pixels of the previous I-frame. This suggests to define a frame containing differences between a P-frame and the previous I-frame, called Δ-frame which has a low quantity of information and hence it can be coded with a low compression rate. A P-frame is decoded via the previous I-frame and the Δ-frame. In the MPEG-4 method [2, 3], that adopts the JPEG technique [4] for coding/decoding frames, the I-frames, P-frames, and B-frames are arranged in a Group of Picture (for short, GOP) sequence. A B-frame is reconstructed by using either the previous or successive I-frame. Here the results of [5] are improved by using a technique based on F-transforms for coding B-frames. For convenience, we assume that the first frame of a video is an I-frame. We assign an ID number to each frame of the video. Then we can say that the th frame is a B-frame or a P-frame if it is “very similar” to the previous th I-frame in the sense that its similarity a parameter