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DCT-domain coder for digital video applications

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Abstract

In this paper, we present an effective DCT-domain video encoder architecture that decreases the computational complexity of conventional hybrid video encoders by reducing the number of transform operations between the pixel and the DCT domains. The fixed video encoder architecture (such as a fixed DCT block of 8 × 8 size) and a huge number of DCT/IDCT transforms performed during the video encoding process limit the minimum possible computational load of conventional video encoders. In this study, we solve this problem by developing a flexible video encoder architecture, which reduces video encoder computational complexity by performing low-resolution coarse-step motion estimation operations in the DCT domain. When a high level of motion activity is detected, the video encoder slightly increases the computational complexity of the motion estimation operation by computing fine-search block matching for a small-size search window in a reference frame. The proposed DCT-domain video encoder architecture is based on the conventional hybrid coder and on a set of fast integer composition and decomposition DCT transforms. The set of transforms implements a technique for estimation of DCT coefficients of a block that is partitioned by the sub-blocks. Experimental results of this method were compared with the results of the conventional hybrid coder in terms of PSNR quality and computational complexity. This comparison shows that the computational complexity of the proposed encoder is lower by 26.8% with respect to the conventional hybrid video coder for the same objective PSNR quality.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, 84105, Beersheba, Israel

    Evgeny Kaminsky

  2. Electro-Optics Unit, Ben-Gurion University of the Negev, 84105, Beersheba, Israel

    Alex Ginzburg

  3. Department of Communication Systems Engineering, Ben-Gurion University of the Negev, 84105, Beersheba, Israel

    Ofer Hadar

Authors
  1. Evgeny Kaminsky
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  2. Alex Ginzburg
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  3. Ofer Hadar
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Corresponding author

Correspondence to Evgeny Kaminsky.

Appendix

Appendix

1.1 Non-zero coefficients of the matrix A

The non-zero coefficients in the transform kernel matrix A can be represented as follows:

$$ \begin{aligned} a & = 1,b = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (\cos ({\pi \mathord{\left/ {\vphantom {\pi {16}}} \right. \kern-\nulldelimiterspace} {16}}) + \cos ({{3\pi } \mathord{\left/ {\vphantom {{3\pi } {16}}} \right. \kern-\nulldelimiterspace} {16}}) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.9808 + 0.8315} \right) = 1.2815, \\ c & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (\cos ({\pi \mathord{\left/ {\vphantom {\pi {16}}} \right. \kern-\nulldelimiterspace} {16}}) - \cos ({{3\pi } \mathord{\left/ {\vphantom {{3\pi } {16}}} \right. \kern-\nulldelimiterspace} {16}}) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.9808 - 0.8315} \right) = 0.1056, \\ d & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {\cos (5\pi /16) + \cos (7\pi /16)} \right) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.5556 + 0.1951} \right) = 0.5308, \\ e & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {\cos (5\pi /16) - \cos (7\pi /16)} \right) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.5556 - 0.1951} \right) = 0.2549, \\ f & = \cos (\pi /8) = 0.9239,g = \cos (3\pi /8) = 0.3827, \\ b & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {\cos (3\pi /16) - \cos (7\pi /16)} \right) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.8315 - 0.1951} \right) = 0.45, \\ i & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {\cos (3\pi /16) + \cos (7\pi /16)} \right) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.8315 + 0.1951} \right) = 0.7259, \\ j & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (\cos ({\pi \mathord{\left/ {\vphantom {\pi {16}}} \right. \kern-\nulldelimiterspace} {16}}) + \cos ({{5\pi } \mathord{\left/ {\vphantom {{5\pi } {16}}} \right. \kern-\nulldelimiterspace} {16}}) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.9808 + 0.5556} \right) = 1.0864{\text{ and}} \\ k & = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (\cos ({\pi \mathord{\left/ {\vphantom {\pi {16}}} \right. \kern-\nulldelimiterspace} {16}}) - \cos ({{5\pi } \mathord{\left/ {\vphantom {{5\pi } {16}}} \right. \kern-\nulldelimiterspace} {16}}) = \sqrt {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \cdot \left( {0.9808 - 0.5556} \right) = 0.3007. \\ \end{aligned} $$

1.2 1-D decomposition transform

The 1-D decomposition transform can be computed by the following 32-equation set.

 

M0 = (Y2 ≪ 1) − Y6;

M8 = Y0 + M0;

M16 = M6 − Y7;

×0 = M8 + M20;

M1 = Y2 + (Y6 ≪ 1);

M9 = Y0 − M0;

M17 = (Y5 ≪3) − Y7;

X6 = M8 − M20;

M2 = (Y1 ≪ 3) − Y7;

M10 = (M2 ≪ 1) + M4;

M18 = Y1 + (Y3 ≪ 3);

X1 = M12 + M21;

M3 = Y1 + (Y7 ≪ 3);

M11 = M2 − (M4 ≪ 1);

M19 = Y1 + M7;

X7 = M21 − M12;

M4 = ((Y3 − Y5) ≪ 3);

M12 = M1 + Y4;

M20 = M10 + M16;

X2 = M9 + M22;

M5 = ((Y3 +Y5) ≪ 3);

M13 = M1 − Y4;

M21 = M14 + M17;

X4 = M9 − M22;

M6 = (Y3 ≪ 1) + Y5;

M14 = M3 + (M5 ≪ 1);

M22 = M11 − M18;

X3 = M13 + M23;

M7 = Y3 − (Y5 ≪ 1);

M15 = (M3 ≪ 1) − M5;

M23 = M15 + M19;

X5 = M23 − M13;

  1. where ≪ denotes the left-shift operation

1.3 1-D composition transform

The 1-D composition transform can be computed by following the 24-equation set.

 

M0 = X0 + X6;

M8 = (((M4 ≪ 1) − M6) ≪ 3);

Y0 = M0 + M2;

M1 = X0 − X6;

M9 = (M1 ≪ 1) + M6;

Y1 = M14 + (M15 ≪ 3) − M3 + M6;

M2 = X2 + X4;

M10 = (M4 ≪ 3) + M1;

Y2 = (M12 ≪ 1) + M13;

M3 = X2 − X4;

M11 = M10 − (M3 ≪ 4);

Y3 = ((M1 − M3) ≪ 3) + M8 + M11;

M4 = X1 + X7;

M12 = M0 − M2;

Y4 = M5 − M7;

M5 = X1 − X7;

M13 = M5 + M7;

Y5 = M8 + M10 − (M11 + M9);

M6 = X3 + X5;

M14 = (M6 ≪ 1) + M4;

Y6 = (M13 ≪ 1) − M12;

M7 = X3 − X5;

M15 = (M1 ≪ 1) + M3;

Y7 = (M14 ≪ 3) − M15 − M4 − M1.

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Kaminsky, E., Ginzburg, A. & Hadar, O. DCT-domain coder for digital video applications. J Real-Time Image Proc 5, 259–274 (2010). https://doi.org/10.1007/s11554-010-0166-5

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