Low-complexity Multidimensional DCT Approximations
This work addresses computational efficiency for video coding and visual tracking applications, but it is incremental as it builds on existing DCT approximations by extending them to higher dimensions.
The paper tackled the problem of high computational complexity in multidimensional discrete cosine transforms (DCT) by introducing low-complexity approximations, resulting in methods that offer almost identical visual quality in video coding and similar performance in visual tracking while significantly reducing arithmetic operations compared to exact 3D DCT.
In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless $8\times 8\times 8$ approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.