A Face Recognition Algorithm Based on Angular Distance Loss Function and Convolutional Neural Network

Xin Long; Hansong Su; Gaohua Liu; Zhenyu Chen

doi:10.3788/LOP55.121505

Journals >Laser & Optoelectronics Progress >Volume 55 >Issue 12 >Page 121505 > Article

Laser & Optoelectronics Progress
Vol. 55, Issue 12, 121505 (2018)

A Face Recognition Algorithm Based on Angular Distance Loss Function and Convolutional Neural Network

Xin Long, Hansong Su, Gaohua Liu^*, and Zhenyu Chen

Author Affiliations

School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China

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DOI: 10.3788/LOP55.121505 Cite this Article Set citation alerts

Xin Long, Hansong Su, Gaohua Liu, Zhenyu Chen. A Face Recognition Algorithm Based on Angular Distance Loss Function and Convolutional Neural Network[J]. Laser & Optoelectronics Progress, 2018, 55(12): 121505 Copy Citation Text

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Fig. 1. Comparison of test protocol of face recognition. (a) Closed-set face recognition; (b) open-set face recognition

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Fig. 2. Comparison of softmax loss function. (a) Traditional softmax loss function; (b) improved softmax loss function

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Fig. 3. Schematic of the proposed angular distance loss function

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Fig. 4. Structure of densely connected networks

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Fig. 5. Comparison of activation functions. (a) ReLU; (b) PReLU

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Fig. 6. Integral structure of network

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Fig. 7. Face recognition accuracy versus hyperparameter ω

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Fig. 8. Test accuracy of LFW dataset for network structures with different layer numbers and different loss functions

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Fig. 9. Test accuracy of LFW dataset for network structures with different layer numbers and widths

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Fig. 10. Proposed implementation process

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Loss function	Decision boundary
Original softmax loss	(W₁-W₂)x+b₁-b₂=0
Modified softmax loss	$\begin{matrix} (x) \end{matrix}$ (cosθ₁-cosθ₂)=0
Angular distance loss	$\begin{matrix} (x) \end{matrix}$ {cosθ₁-cos[(1-ω)θ₂]}=0 for class 1
Angular distance loss	$\begin{matrix} (x) \end{matrix}$ {cos[(1-ω)θ₁]-cosθ₂}=0 for class 2

Table 1. Comparison of classification boundaries of loss functions

Layer	Output size	DenseFace-42	DenseFace-54	DenseFace-78	DenseFace-122
Dense block 1	56×56	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×4	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6
Dense block 2	28×28	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×5	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×12	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×12
Dense block 3	14×14	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×5	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×12	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×24
Dense block 4	7×7	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×4	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×6	$\begin{matrix} [\begin{matrix} 1 \times 1 \\ 3 \times 3 \end{matrix}] \end{matrix}$ ×16

Table 2. Specific configuration of the dense connection structure

Net structure	Input size /pixel	Depth /layer	Parameter /10⁶
LeNet	32×32×1	5	0.062
AlexNet	227×227×3	8	62.4
VGGNet	224×224×3	16	138.4
GoogleNet	224×224×3	22	5.3
ResNet	224×224×3	152	61.3
DenseFace (width: 32)	112×112×3	42	6.7
		54	7.3
		78	8.9
		122	12.8
DenseFace (width: 16)	112×112×3	42	5.78
		54	5.9
		78	6.37
		122	7.4

Table 3. Comparison of parameter quantities of several convolutional neural network models

Method	Dataset	Data amount /10⁶	Accuracy /%
DeepFace	LFW	4	97.33
FaceNet	LFW	200	99.67
Deep FR	LFW	2.6	98.85
DeepID2+	LFW	0.3	98.74
Center Face	LFW	0.7	99.31
Softmax loss	CAISA-WebFace	0.49	97.78
Triplet loss	CAISA-WebFace	0.49	98.65
Center loss	CAISA-WebFace	0.49	99.02
L-softmax loss	CAISA-WebFace	0.49	99.15
Angular distance loss	CAISA-WebFace	0.49	99.45

Table 4. Test accuracy of different loss functions or face recognition algorithms

Method	Test protocol	Accuracy /%
Method	Test protocol	Face identification	Face verification
FaceNet	large	70.496	86.473
Deepsense	large	74.798	87.764
Deepsense	small	70.983	82.851
Softmax loss	small	54.628	65.732
Triplet loss	small	64.698	78.030
Center loss	small	65.334	80.106
L-softmax loss	small	67.035	80.185
Angular softmax loss	small	72.534	85.348

Table 5. Test accuracy of different loss functions or face recognition algorithms on the MegaFace dataset

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