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Estimation of Automotive Pitch, Yaw, and Roll using Enhanced Phase Correlation on Multiple Far-field Windows M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester Visual Sensorics and Information Processing Lab Goethe-University, Frankfurt

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SLIDE 1

Estimation of Automotive Pitch, Yaw, and Roll using Enhanced Phase Correlation on Multiple Far-field Windows

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

Visual Sensorics and Information Processing Lab Goethe-University, Frankfurt and Computer Vision Laboratory Link¨

  • ping University, Sweden

July 22, 2015

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 2

Motion estimation

From far-field sub-images at two instants t − 1 and t, the module determines: Global 2D translational motion Rate changes in the camera angle (roll/pitch/yaw) Rotation matrix between t − 1 and t The motion is analysed for each pair of corresponding windows at instants t − 1 and t

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 3

System Overview

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 4

Structure test

The motion is only measured on those cells with enough structure

  • information. To find those, we compute the windowed average

ˆ mk = 1

  • xi wT(xi) ·

M

  • i=1

wT(xi) · s(xi) (1) and the variance: ˆ σ2

k =

1

  • xi wT(xi) ·

M

  • i=1

wT(xi) · (s(xi) − ˆ mk)2 (2) Further computations are performed only on cells with sufficient structure. ˆ σ2

k too weak structure

< >

sufficient structure

Tvar (3)

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 5

Determining the translation motion

We use a regularized version of Phase-only-Correlation. P(f) = S(f) · G∗(f) |S(f) · G∗(f)| + λ (4) Where lamba performs a soft thresholding of the FFT, leaving almost intact the votes from amplitudes larger than lambda and giving small weight to the rest. The displacement d between cells is determined as the location of the maximum of the inverse Fourier transform of P(f): p(x) = F−1{P(f)} ≃ δ(x − d) (5)

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 6

Thresholding the back-projected spectrum

Due to non-pure translation motion, the back-projected spectrum might not concentrate in one peak. We compute the variance of the noise σ2

n = 1

M p(x)2

F

(6) and then we select a subset P of pixel coordinates belonging to the pixels of the peaks that passed the test p(x)

!

> 5 · σn ∧ p(x)

!

> 0.6 · max(p(x)) (7)

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 7

Checking the compactness of the peaks

To find the peak compactness, the image intensity is normalized h(x) =    p(x)/

x∈P

p(x) , x ∈ P , else (8) We first determine the centroids µ = (µ1, µ2) of h(x) µ =

  • x

h(x) · x (9) and then the compactness K is computed as the sum of the 2nd

  • rder moments in both directions

K =

  • x

h(x) · x − µ2

2

(10) We test the compactness K and only the compact cells are used afterwards K

compact

< >

not compact

Tcomp (11)

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 8

Estimating the roll angle

We define the matrix A with the centres of the windows and matrix B with position after applying the displacement d Both sets of points are aligned to the origin of coordinates by A′ = A − 1 k

k

  • i=1

ci B′ = B − 1 k

k

  • i=1

c′

i

(12)

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 9

Estimating the roll angle

We find the rotation matrix R that minimizes the element-wise difference of the points in A′ and the rotated points in B′: min A′R − B′F (13) From the sought rotation matrix R: R = cos(Φ) − sin(Φ) sin(Φ) cos(Φ)

  • (14)

We obtain the roll angle Φ according to: Φ = arctan (R2,1, R1,1) (15)

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 10

Estimating the roll angle

Additionally we determine the average translation ¯ d between the point sets A and B, for latter estimating the pitch and yaw angles: ¯ d = 1 k

k

  • i=1

(c′

i − ci) = 1

k

k

  • i=1

di (16) The transformation T = (R, ¯ d) maps the B points into A.

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 11

Testing the validity of the mapping

We validate if the mapping of the point sets is correct: 1 k

k

  • i=1

T · ci − c′

i2 2 valid

< >

not valid

Tdist (17) If the distance is too large, we iteratively repeat the previous process using a leave-one-out strategy and we take the motion vector with the smallest distance

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 12

Finding pitch and yaw angles

  • p2
  • p1

α f H2 H1 f x

  • p1
  • p2

x α f H

The pitch θ and yaw Ψ are computed as: θ = arctan cx − p′

2x

fx

  • − arctan

cx − p′

1x

fx

  • (18)

Ψ = arctan cy − p′

2y

fy

  • − arctan

cy − p′

1y

fy

  • (19)
  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 13

Motion results

Estimation of camera angles for Kitti sequence 3

50 100 150 200 250 −0.5 0.5 1 frame number

  • rel. roll rate [deg/frame]

gt estim.

50 100 150 200 250 −0.5 0.5 1 frame number

  • rel. pitch rate [deg/frame]

gt estim.

50 100 150 200 250 −2 2 4 frame number

  • rel. yaw rate [deg/frame]

gt estim.

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 14

Motion results

Estimation of camera angles for Kitti sequence 7

800 850 900 950 1000 1050 −1 −0.5 0.5 frame number

  • rel. roll rate [deg/frame]

gt estim.

800 850 900 950 1000 1050 −1 −0.5 0.5 frame number

  • rel. pitch rate [deg/frame]

gt estim.

800 850 900 950 1000 1050 −4 −2 2 frame number

  • rel. yaw rate [deg/frame]

gt estim.

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 15

Motion results

Table with results for the KITTI odometry sequences

Roll Pi/Ya Pitch Yaw Seq Valid

  • Est. E

Corr Valid

  • Est. E

Corr

  • Est. E

Corr 96.19 0.121 0.631 99.98 0.044 0.963 0.133 0.991 1 99.18 0.078 0.577 99.91 0.024 0.949 0.068 0.99 2 93.84 0.159 0.5 99.98 0.053 0.951 0.126 0.987 3 97.99 0.086 0.754 99.87 0.038 0.968 0.098 0.985 4 94.78 0.142 0.395 99.63 0.04 0.873 0.121 0.193 5 98.37 0.108 0.509 99.96 0.033 0.966 0.114 0.989 6 98.45 0.089 0.503 99.91 0.026 0.968 0.105 0.994 7 97.63 0.1 0.608 99.91 0.03 0.965 0.151 0.922 8 95.82 0.104 0.62 99.98 0.034 0.965 0.123 0.991 9 94.08 0.136 0.524 99.94 0.04 0.953 0.125 0.987 10 93.41 0.139 0.537 99.92 0.04 0.974 0.121 0.986

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 16

Conclusions

What we achieved: A reliable method for determining 2D global motion vectors and rotation angles for a pair of consecutive frames of an automotive sequence. An algorithm which can run on real-time (20-25fps) and assist

  • n the prediction of tracked keypoints.
  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 17

Future work

Boost the accuracy of the 2D motion estimates by using sub-pixel measurements. Choose among multiple hypotheses from phase correlation. Measure the motion in more windows, and use depth estimates from SfM of previous frame. Use more complex consistency checks to reduce outliers still further.

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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SLIDE 18

Contact

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

barnada,conrad,bradler,ochs,mester@vsi.cs.uni-frankfurt.de http://www.vsi.cs.uni-frankfurt.de http://www.cvl.isy.liu.se/

  • M. Barnada, C. Conrad, H. Bradler, M. Ochs and R. Mester

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