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A new perceptual video fingerprinting system

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Abstract

Search, retrieval and storage of video content over the Internet and online repositories can be efficiently improved using compact summarizations of this content. Robust and perceptual fingerprinting codes, extracted from local video features, are astutely used for identification and authentication purposes. Unlike existing fingerprinting schemes, this paper proposes a robust and perceptual fingerprinting solution that serves both video content identification and authentication. While content identification is served by the robustness of the proposed fingerprinting codes to content alterations and geometric attacks, their sensitivity to malicious attacks makes them fit for forgery detection and authentication. This dual usage is facilitated by a new concept of sequence normalization based on the circular shift properties of the discrete cosine and sine transforms (DCT and DST). Sequences of local features are normalized by estimating the circular shift required to align each of these sequences to a reference sequence. The fingerprinting codes, consisting of normalizing shifts, are properly modeled using information-theoretic concepts. Security, robustness and sensitivity analysis of the proposed scheme is provided in terms of the security of the secret keys used during the proposed normalization stage. The computational efficiency of the proposed scheme makes it appropriate for large scale and online deployment. Finally, the robustness (identification-based) and sensitivity (authentication-based) of the proposed fingerprinting codes to content alterations and geometric attacks is evaluated over a large set of video sequences where they outperform existing DCT-based codes in terms of robustness, discriminability and sensitivity to moderate and large size intentional alterations.

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Notes

  1. Our proposed fingerprinting scheme is based on a modified version of the DLBM-based one as shown in Section 4.4.

  2. The best SVD numerical implementations have a complexity order of O(m i n(m n 2, m 2 n)) on m × n matrices [13].

  3. The feature point-based technique extracts the 64 most robust features from image corners and edges [38].

  4. Typical frame rates are usually 60 or 30 fps [22].

  5. The DLBM concept, attributed to Oostoven et al. [43] is extended in this paper to cover all spatial and temporal directions in the fingerprinting code extraction.

  6. The sizes of F h o r , F v e r and F t e m p are R × (C − 1), (R − 1) × C and R × C, respectively.

  7. Using the z-transform concepts, the proof of (18)-(19) is provided in Appendix.

  8. To enhance the security of our proposed video fingerprinting solution, the random generator is set using a secret key K 1 ∈ 𝕂.

  9. L represents the number of frames in the video sequence after the frame rate is reduced to 5 fps in the preprocessing stage.

  10. The first bit in \( bin\_h_{K_{1}} \) is set to 1.

  11. It is assumed that the number of frames, L, is larger than the height of the block in each frame R.

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Acknowledgment

The author would like to thank King Fahd University of Petroleum and Minerals for supporting this work.

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Correspondence to Lahouari Ghouti.

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This research is supported by King Fahd University of Petroleum and Minerals.

Appendix A: Proof of (18)–(19)

Appendix A: Proof of (18)–(19)

In this appendix, we will provide the proof of (18)–(19)

Let \( \{ x_{0}(n) \}_{n = -0}^{N - 1} \) and \( \{ x_{1}(n) \}_{n = -0}^{N - 1} \) be an N-length sequence and its one-sample circularly-shifted version such as:

$$ \{ x_{0}(n) \}_{n = 0}^{N - 1} = \{ x_{0}(0), x_{0}(1), \ldots, x_{0}(N - 1) \} $$
(49)
$$ \{ x_{1}(n) \}_{n = 0}^{N - 1} = \{ x_{0}(1), x_{0}(2), \ldots, x_{0}(N - 1), x_{0}(0) \} $$
(50)

The z-transforms of the sequences, defined in (49)–(50) are given by [41]:

$$ X_{0}(z) = \sum\limits_{n = 0}^{N - 1} x_{0}(n) z^{-n} $$
(51)
$$ X_{1}(z) = \sum\limits_{n = 0}^{N - 1} x_{1}(n) z^{-n} $$
(52)

where \( z = x + j \cdot y \in \mathbb {C} \) and j 2 = −1.

Using (50), (52) is expanded as follows:

$$ X_{1}(z) = x_{0}(1) + x_{0}(2) \cdot z^{-1} + {\cdots} + x_{0}(N_{1}) \cdot z^{-(N - 2)} + x_{0}(0) \cdot z^{-(N - 1)} $$
(53)

To relate X 1(z) to X 0(z), let us multiply both terms of (51) by z:

$$ z \cdot X_{0}(z) = x_{0}(0) \cdot z + x_{0}(1) + x_{0}(2) \cdot z^{-1} + {\cdots} + x_{0}(N - 1) \cdot z^{-(N - 2)} $$
(54)

Equation (54) can be written in terms of X 1(z) using the following equality:

$$ x_{0}(1) + x_{0}(2) \cdot z^{-1} + {\cdots} + x_{0}(N - 1) \cdot z^{-(N - 2)} = X_{1}(z) - x_{0} \cdot z^{-(N - 1)} $$
(55)
$$ z \cdot X_{0}(z) = x_{0}(0) \cdot z + X_{1}(z) - x_{0} \cdot z^{-(N - 1)} $$
(56)

Then, X 1(z) is expressed as:

$$ X_{1}(z) = z \cdot X_{0}(z) + x_{0}(0) \left[ z^{-(N - 1)} - z \right] $$
(57)

Equation (16), that defines the one-sample circular shift property, is reproduced below for ease of reference:

$$\begin{array}{@{}rcl@{}} \mathcal{X}_{k+1} = \mathcal{A} \cdot \mathcal{X}_{k} \end{array} $$
(58)

where

$$\begin{array}{@{}rcl@{}} \mathcal{X}_{k+1} = \left[\begin{array}{c} X_{k+1}^{C_{2}}(m) \\ X_{k+1}^{S_{2}}(m - 1) \end{array}\right], \; \; \; \; \mathcal{A} = \left[\begin{array}{cc} \cos(v) & \sin(v) \\ -\sin(v) & \cos(v) \end{array}\right], \; \; \; \; \mathcal{X}_{k} = \left[\begin{array}{c} X_{k}^{C_{2}}(m) \\ X_{k}^{S_{2}}(m - 1) \end{array}\right] \end{array} $$
(59)

where \( v = \frac {m \pi }{N} \).

Using the shift property of the z-transform (see (57), the matrix form of the z-transform of (58) gives:

$$\begin{array}{@{}rcl@{}} \left( z \cdot \mathbf{I}_{2 \times 2} - \mathcal{A} \right) \cdot \mathcal{X}_{k}(z) = \mathbf{I}_{2 \times 2} \left( z - z^{-(N - 1)} \right) \cdot \mathcal{X}_{0} \end{array} $$
(60)

where \( \mathcal {X}_{k}(z) \) and I 2×2 represent the matrix-form z-transform of \( \mathcal {X}_{k}(z) \) and the 2 × 2 identity matrix, respectively.

Equation (60) is further simplified into:

$$\begin{array}{@{}rcl@{}} \mathcal{X}_{k}(z) = \left( z \cdot \mathbf{I}_{2 \times 2} - \mathcal{A} \right)^{-1} \cdot \left( z - z^{-(N - 1)} \right) \cdot \mathcal{X}_{0} \end{array} $$
(61)

Therefore, \( \mathcal {X}_{k}(z) \) is given by:

$$\begin{array}{@{}rcl@{}} \mathcal{X}_{k}(z) = \left( \begin{array}{cc} \frac{z - \cos(v)}{1 - 2 \cos(v)z + z^{2}} & \frac{\sin(v)}{1 - 2 \cos(v)z + z^{2}} \\ -\frac{1}{1 - 2 \cos(v)z + z^{2}} & \frac{1}{1 - 2 \cos(v)z + z^{2}} \end{array} \right) \cdot \left( z - z^{-(N - 1)} \right) \cdot \mathcal{X}_{0} \end{array} $$
(62)

To get \( \mathcal {X}_{k} \), the inverse z-transform is applied on (62) as follows:

$$\begin{array}{@{}rcl@{}} \mathcal{X}_{k} = \left[ \begin{array}{c} X_{0}^{C_{2}}(m) \cos(v \cdot k) + X_{0}^{S_{2}}(m - 1) \cdot \sin(v \cdot k) \\ -X_{0}^{C_{2}}(m) \sin(v \cdot k) + X_{0}^{S_{2}}(m - 1) \cdot \cos(v \cdot k) \end{array} \right] \end{array} $$
(63)

Finally, (63) can be rewritten in its final form:

$$\begin{array}{@{}rcl@{}} \mathcal{X}_{k} = \left[ \begin{array}{c} \sqrt{\left[ X_{0}^{C_{2}}(m) \right]^{2} + \left[ X_{0}^{S_{2}}(m - 1) \right]^{2}} \cdot \cos \left( v \cdot k - \arctan \left[ \frac{X_{0}^{S_{2}}(m - 1)}{X_{0}^{C_{2}(m)}} \right] \right) \\ \sqrt{\left[ X_{0}^{C_{2}}(m) \right]^{2} + \left[ X_{0}^{S_{2}}(m - 1) \right]^{2}} \cdot \cos \left( v \cdot k - \arctan \left[ -\frac{X_{0}^{C_{2}(m)}}{X_{0}^{S_{2}}(m - 1)} \right] \right) \end{array} \right] \end{array} $$
(64)

The elements of (64) represent (18)–(19) which concludes our proof.

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Ghouti, L. A new perceptual video fingerprinting system. Multimed Tools Appl 77, 6713–6751 (2018). https://doi.org/10.1007/s11042-017-4595-z

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