過去三十年已刊登超過3000篇關於光流算法的文章。我們試圖對最近光流算法的技術成果提供可理解的探討。近期的主要出版物包括光流不同方面的研究，包括差分型和區塊匹配為基礎的方法都在這次探討裏面。我們確定了一些光流的應用，如流量分析和車輛追蹤、接觸時間。我們查證幾個公開的光流程式：Farneback、Lukas-Kanad、Horn-Schunck、TVL1，並顯示其結果。執行Classic+NL-Fast時，孫得清博士等人使用5點微分濾波器 [-1, 8, 0, -8, 1] 計算第二張影像的導數，平均角度誤差是2.401度，端點誤差是0.076。我們使用5點微分濾波器 [2, -10, 0, 10, -2]，獲得更好的結果：平均角度誤差是2.272度，端點誤差是0.073。

More than 3000 articles on optical flow algorithms have been published in the past thirty years. We attempt to provide a comprehensible survey of the recent technical achievements in optical flow algorithms. Major recent publications are included in this survey covering different aspects of the research in this area, including differential-based and block matching-based methods. We identify several applications of optical flow, such as Traffic Analysis and Vehicle Tracking, time-to-contact. We investigate several public optical flow codes: Farneback, Lukas-Kanad, Horn-Schunck, TVL1, Classic+NL-Fast; and show their results of experiments. When running Classic+NL-Fast (proposed by Deqing Sun et al.), they compute the derivatives of the second image using the 5-point derivative filter [-1, 8, 0, -8, 1]. The estimated flow field on "RubberWhale" has an average angular error (AAE) of 2.401 degrees and an average end point error (EPE) of 0.076. We compute the derivatives using the 5-point derivative filter [2, -10, 0, 10, -2], and obtain better result with AAE of 2.272 degrees and average EPE of 0.073.

CONTENTS
ABSTRACT IN CHINESE…………………………………………………………… I
ABSTRACT IN ENGLISH……………………………………………………………Ⅱ
ACKNOWLEDGEMENTS……………………………………………………………Ⅲ
CONTENTS ………………………………………………………………………… Ⅳ
LIST OF FIGURES……………………………………………………………………Ⅵ
Chapter 1 Introduction………………………………………………………………… 1
1.1 Overview……………………………………………………………………… 1
1.2 Aperture Problem……………………………………………………………… 2
1.3 Ground Truth Generation……………………………………………………… 2
1.4 Performance metrics…………………………………………………………… 3
1.5 Stereo correspondence visualization…………………………………………… 5
Chapter 2 Methods of Optical Flow Computation…………………………………… 7
2.1 Differential method…………………………………………………………… 7
2.1.1 Lucas–Kanade method…………………………………………………… 7
2.1.2 Horn–Schunck method……………………………………………………… 8
2.1.3 Variational methods…………………………………………………………10
2.2 Block Matching……………………………………………………………… 10
2.3 Discrete optimization………………………………………………………… 11
Chapter 3 The Applications of Optical Flow Algorithms………………………………12
3.1 Time to Contact and Focus of Expansion………………………………………12
3.2 Motion Parameters and Depth………………………………………………… 12
3.3 Segmentation………………………………………………………………… 12
3.4 Traffic Analysis and Vehicle Tracking……………………………………… 12
3.5 Face Tracking…………………………………………………………………13
3.6 Detection and Tracking of Moving Blobs………………………………………13
3.7 Optical Flow by Dynamic Region Matching……………………………………14
3.8 Occlusion Analysis by Pixel Contention……………………………………… 14
3.9 The Integration of Optical Flow and Deformable Models………………………14
3.10 The Use Of Optical Flow For Road Navigation………………………………15
3.11 Fluid experimental flow estimation based on an optical-flow scheme…………15
3.12 Optical Flow Based Navigation………………………………………………15
Chapter 4 Software and Our Experimental Results…………………………………… 16
4.1 Farneback Optical Flow………………………………………………………16
4.2 Lukas-Kanade Optical Flow………………………………………………… 17
4.3 Horn-Schunck optical flow……………………………………………………18
4.4 TVL1 Optical Flow ………………………………………………………… 19
4.5 IVANN…………………………………………………………………… … 20
4.6 Simpleflow……………………………………………………………………21
4.7 Constrained Optical Flow Estimation (COFM)…………………………………21
4.8 Classic+NL-Fast ………………………………………………………………23
4.8.1 Filter used in Wedel etal "improved TV L1"………………………………… 23
4.8.2 Modified Filter …………………………………………………………… 24
Chapter 5 Conclusions……………………………………………………………… 25
Appendix …………………………………………………………………………… 26
A.1 Lucas-Kanade algorithm………………………………………………………26
A.2 Partial result of Pyramidal Horn-Schunck algorithm ………………………… 28
A.3 Partial result of Simpleflow……………………………………………………28
REFERENCES ……………………………………………………………………… 31

























LIST OF FIGURES
Fig. 1.1 Barber''s pole……………………………………………………………………2
Fig. 1.2 Average end point error on Middlebury flow benchmark-left part (Jul. 1st 2014) 4
Fig. 1.3 Average EPE on Middlebury flow benchmark-right part (Jul. 1st 2014)…………4
Fig. 1.4 Average EPE on Middlebury flow benchmark (rank 85th)………………………5
Fig. 1.5 (a) a specific disparity………………………………………………………… 5
Fig. 1.5 (b) a specific optical flow vector……………………………………………… 5
Fig. 1.6 Overlay of correspondence visualizations and reference images…………………6
Fig 2.1 Graphical display of the optical flow contraint equation………………………… 9
Fig. 3.1 Output image for optical flow…………………………………………………13
Fig. 4.1 Optical flow vector……………………………………………………………16
Fig. 4.2 (a) A taxi in Hamburg…………………………………………………………16
Fig. 4.2 (b) Optic flow of (a) ………………………………………………………… 16
Fig. 4.3 (a) Durlacher-Tor …………………………………………………………… 17
Fig. 4.3 (b) Optic flow of (a) ………………………………………………………… 17
Fig. 4.4 (a) Ettlinger-Tor………………………………………………………………17
Fig. 4.4 (b) Optic flow of (a) ………………………………………………………… 17
Fig. 4.5 (a) Lucas-Kanade algorithm ………………………………………………… 18
Fig. 4.5 (b) Optic flow vectors for Hybrid Median filtered images …………………… 18
Fig. 4.6 Optical flow example (the code is listed in A.1)……………………………… 18
Fig. 4.7 (a) Input1 …………………………………………………………………… 19
Fig. 4.7 (b) Input2 …………………………………………………………………… 19
Fig. 4.7 (c) Optic flow…………………………………………………………………19
Fig. 4.8 Result for the Middlebury test sequences (Hydrangea)…………………………20
Fig. 4.9 Result for the Middlebury test sequences (Venus) …………………………… 20
Fig. 4.10 (a) Grove-IVANN flow………………………………………………………21
Fig. 4.10 (b) Grove-IVANN flow error ……………………………………………… 21
Fig. 4.11 (a) Down sampling image for Venus…………………………………………21
Fig. 4.11 (b) Original image "Venus"………………………………… ……………… 21
Fig. 4.12 Resultant OF…………………………………………………………………22
Fig. 4.13 Estimated flow fields on sequence "RubberWhale" using Classic+NL ……… 24

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