﻿ 基于优化图的半监督学习的行人检测

# 基于优化图的半监督学习的行人检测Pedestrian Detection Based on Optimized Semi-Supervised Learning Method

Abstract: Pedestrian detection remains one of the challenging tasks in the area of computer vision. In order to improve the effectiveness of pedestrian detection, this paper proposes a new approach to pedestrian detection. First, the shape context features of each image are represented. Then, we specifically design a novel optimized graph-based semi-supervised learning for pedestrian detection, in which we maximize the average weighed distance between the suggestion box with pedestrians and the suggestion box without pedestrians, and minimize the average weighed distance between the suggestion boxes with pedestrian. Training data insufficiency and lack of generalization of learning method can be resolved. Compared with several other approaches, the experimental results show that this approach performs more effectively and accurately.

1. 引言

2. 图的半监督学习理论

${w}_{ij}=\left\{\begin{array}{l}\mathrm{exp}\left(-\frac{{‖{x}_{i}-{x}_{j}‖}^{2}}{\sigma }\right),\text{ }\text{if}\text{ }\text{\hspace{0.17em}}{x}_{i}\ne {x}_{j}\\ 0\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{otherwise}\end{array}$ (1)

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${L}^{*}\left(f\right)=\mathrm{min}\left\{\underset{i=1}{\overset{l}{\sum }}L\left(f\left({x}_{i}\right),{y}_{i}\right)\right\}$ (3)

$s\left(f\right)={f}^{\prime }Lf=\underset{i,j=1}{\overset{n}{\sum }}{w}_{ij}{\left(\frac{f\left({x}_{i}\right)}{\sqrt{{d}_{i}}}-\frac{f\left({x}_{j}\right)}{\sqrt{{d}_{j}}}\right)}^{2}$ (4)

$\begin{array}{c}{f}^{*}=\mathrm{arg}\underset{f\left({x}_{i}\right)}{\mathrm{min}}\left\{s+\gamma {L}^{*}\right\}\\ =\mathrm{arg}\underset{f\left({x}_{i}\right)}{\mathrm{min}}\left\{{f}^{\prime }Lf+\gamma \underset{i=1}{\overset{l}{\sum }}L\left(f\left({x}_{i}\right),{y}_{i}\right)\right\}\end{array}$ (5)

3. 基于优化的半监督学习的行人检测算法

3.1. 特征提取和行人候选区域选取

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3.2. 优化图的半监督学习模型的构建

3.2.1. 构建优化图的半监督行人检测模型

$\mathrm{min}\underset{i=1}{\overset{{l}^{+}}{\sum }}\underset{j=1}{\overset{{l}^{+}}{\sum }}{w}_{i,j}$ (7)

$\mathrm{max}\underset{i=1}{\overset{{l}^{+}}{\sum }}\underset{j={l}^{+}}{\overset{{l}^{-}}{\sum }}{w}_{i,j}$ (8)

$W=\mathrm{arg}\underset{{w}_{i,j}}{\mathrm{min}}\underset{i=1}{\overset{l}{\sum }}\underset{j=1}{\overset{l}{\sum }}{h}_{i,j}{w}_{i,j}$ (9)

${h}_{ij}=\left\{\begin{array}{l}1,\text{ }\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}1\le i,j\le {l}^{+}\\ -1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}1\le i\le {l}^{+};\text{\hspace{0.17em}}{l}^{+} (10)

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3.2.2. 优化图的半监督行人检测模型的分析

$\underset{\omega ,b}{\mathrm{min}}\underset{i=1}{\overset{l}{\sum }}\underset{j=1}{\overset{l}{\sum }}{\left({{w}^{\prime }}_{i,j}-〈\omega \cdot {x}_{i,j}〉-b\right)}^{2}$ (12)

$\begin{array}{l}\underset{w,b}{\mathrm{min}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{2}{‖\omega ‖}^{2}\\ \text{s}\text{.t}\text{.}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\left(\omega \cdot {x}_{i,j}\right)+b\right)-{{w}^{\prime }}_{i,j}\le \epsilon ,i,j=1,\cdots ,l\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{{w}^{\prime }}_{i,j}-\left(\left(\omega \cdot {x}_{i,j}\right)+b\right)\le \epsilon ,i,j=1,\cdots ,l\end{array}$ (13)

$\begin{array}{l}L\left(\omega ,b,{\alpha }^{\left(*\right)}\right)=\frac{1}{2}{‖\omega ‖}^{2}-\underset{i=1}{\overset{l}{\sum }}\underset{j=1}{\overset{l}{\sum }}{\alpha }_{i,j}\left(\epsilon +{{w}^{\prime }}_{i,j}-\left(\omega \cdot {x}_{i,j}\right)-b\right)\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}\text{ }\text{\hspace{0.17em}}-\underset{i=1}{\overset{l}{\sum }}\underset{j=1}{\overset{l}{\sum }}{\alpha }_{i,j}^{*}\left(\epsilon -{{w}^{\prime }}_{i,j}+\left(\omega \cdot {x}_{i,j}\right)+b\right)\end{array}$ (14)

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$\begin{array}{l}\underset{a,{a}^{\left(*\right)}}{\mathrm{min}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{2}\underset{i=1}{\overset{l}{\sum }}\underset{j=1}{\overset{l}{\sum }}\underset{m=1}{\overset{l}{\sum }}\underset{n=1}{\overset{l}{\sum }}\left({a}_{i,j}^{*}-{a}_{i,j}\right)\left({a}_{m,n}^{*}-{a}_{m,n}\right)\left({x}_{i,j}\cdot {x}_{m,n}\right)-\epsilon \underset{i,j=1}{\overset{l}{\sum }}\left({a}_{i,j}^{*}+{a}_{i,j}\right)\\ \text{s}\text{.t}\text{.}\text{ }\underset{i=1,j}{\overset{l}{\sum }}\left({a}_{i,j}-{a}_{i,j}^{*}\right)=0,\\ \text{ }\text{ }{a}_{i,j}^{\left(*\right)}\ge 0,i,j=1,\cdots ,l\end{array}$ (16)

${w}^{″}\left({x}_{i,j}\right)=\underset{i=1}{\overset{l}{\sum }}\underset{j=1}{\overset{l}{\sum }}\left({\alpha }_{i,j}^{*}-{\alpha }_{i,j}\right)\left(x\cdot {x}_{i,j}\right)+b$ (17)

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4. 实验结果及分析

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$\text{precision}=\frac{{N}_{c}}{{N}_{c}+{N}_{f}}$ (21)

Figure 1. Log-Polar Transformation. (a) Direction of 0˚ Log-Polar Transformation; (b) Direction of 45˚ Log-Polar Transformation; (c) Direction of 90˚ Log-Polar Transformation; (d) Direction of 135˚ Log-Polar Transformation

Figure 2. Log-Polar coordinate histogram

Table 1. Experiment Comparison with SC + GLSS

Table 2. Experiment Comparison with HOG + SVM

5. 结束语

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