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The use of the symmetric finite difference in the local binary pattern (symmetric LBP)

Zeinab Sedaghatjoo, Hossein Hosseinzadeh

TL;DR

This work addresses the high dimensionality of Local Binary Pattern (LBP) descriptors by introducing a symmetric finite-difference approach to directional derivatives, enabling a 4-bit symmetric LBP (SyLBP4) and a related 8-bit symmetric LBP (SyLBP8) alongside the standard LBP (StLBP). The core finding is that under symmetric finite differences $d_i = -d_{i+4}$, causing strong correlation between $H(d_i)$ and $H(d_{i+4})$, which motivates discarding the first four directions and using only $d_5$–$d_8$, yielding $lbp = \sum_{i=1}^{4} 2^{i-1} H(d_{i+4})$ with 16 patterns. Experiments on CFD, CFD-MR, CFD-INDIA and CK with SVM classifiers show that SyLBP4 achieves comparable accuracy to StLBP while using far fewer features, illustrating substantial efficiency gains for face detection and expression recognition. The study suggests further exploration of larger block sizes and higher-order derivatives to extend the benefits to broader datasets and applications, potentially enhancing performance without increasing feature dimensionality dramatically.

Abstract

The paper provides a mathematical view to the binary numbers presented in the Local Binary Pattern (LBP) feature extraction process. Symmetric finite difference is often applied in numerical analysis to enhance the accuracy of approximations. Then, the paper investigates utilization of the symmetric finite difference in the LBP formulation for face detection and facial expression recognition. It introduces a novel approach that extends the standard LBP, which typically employs eight directional derivatives, to incorporate only four directional derivatives. This approach is named symmetric LBP. The number of LBP features is reduced to 16 from 256 by the use of the symmetric LBP. The study underscores the significance of the number of directions considered in the new approach. Consequently, the results obtained emphasize the importance of the research topic.

The use of the symmetric finite difference in the local binary pattern (symmetric LBP)

TL;DR

This work addresses the high dimensionality of Local Binary Pattern (LBP) descriptors by introducing a symmetric finite-difference approach to directional derivatives, enabling a 4-bit symmetric LBP (SyLBP4) and a related 8-bit symmetric LBP (SyLBP8) alongside the standard LBP (StLBP). The core finding is that under symmetric finite differences , causing strong correlation between and , which motivates discarding the first four directions and using only –, yielding with 16 patterns. Experiments on CFD, CFD-MR, CFD-INDIA and CK with SVM classifiers show that SyLBP4 achieves comparable accuracy to StLBP while using far fewer features, illustrating substantial efficiency gains for face detection and expression recognition. The study suggests further exploration of larger block sizes and higher-order derivatives to extend the benefits to broader datasets and applications, potentially enhancing performance without increasing feature dimensionality dramatically.

Abstract

The paper provides a mathematical view to the binary numbers presented in the Local Binary Pattern (LBP) feature extraction process. Symmetric finite difference is often applied in numerical analysis to enhance the accuracy of approximations. Then, the paper investigates utilization of the symmetric finite difference in the LBP formulation for face detection and facial expression recognition. It introduces a novel approach that extends the standard LBP, which typically employs eight directional derivatives, to incorporate only four directional derivatives. This approach is named symmetric LBP. The number of LBP features is reduced to 16 from 256 by the use of the symmetric LBP. The study underscores the significance of the number of directions considered in the new approach. Consequently, the results obtained emphasize the importance of the research topic.
Paper Structure (5 sections, 8 equations, 4 figures, 2 tables)

This paper contains 5 sections, 8 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Local Binary Pattern
  3. Directional derivatives and the symmetric LBP
  4. Experiment results and discussions
  5. Conclusion

Figures (4)

  • Figure 1: Directional derivatives respect to the standard LBP (A), 8-bit symmetric LBP (B) and 4-bit symmetric LBP (C).
  • Figure 2: The correlation matrix showing the correlation coefficients between variables $H(d_i)$ for a face image. The coefficients between $H(d_i)$ and $H(d_{i+4})$ is less than $-0.94$ highlights the linear dependency between the variables.
  • Figure 3: The histogram respect to StLBP, SyLBP8 and SyLBP4 within a global and a local images is presented from left to right, respectively.
  • Figure 4: Some human faces for face detection (left) and facial expression recognition (right). These images are presented in CFD, CFD-MR, CFD-INDIA and CK datasets.