Abstract

In this paper the registration mapping function is derived for images that are produced by parallel projections. This function has the form F(x, y) = A(x, y) + h(x, y)e, where A(x, y) is an affine transformation, h(x, y) is a scalar-valued function, and e is a vector that defines the epipolar lines. The main result of the paper is the formulation of a normalization constraint that guarantees the uniqueness of the parameters of this function and makes possible their least-squares estimation from a collection of matching points. This approach reduces the search for match points from a two-dimensional to a one-dimensional search along the epipolar lines, thereby increasing the accuracy and robustness of image registration. Simulation results are presented that demonstrate the validity of this approach for nonparallel as well as for parallel imaging geometries. Subpixel registration accuracy is possible for perspective projections as long as either the field of view or the separation angle between the two images is small.

© 1993 Optical Society of America

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References

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  1. J. Ton, A. K. Jain, “Registering Landsat images by point matching,”IEEE Trans. Geosci. Remote Sensing 27, 642–651 (1989).
    [CrossRef]
  2. J. Owczarczyk, W. J. Welsh, S. Searby, “Performance analysis of image registration techniques,” in Third International Conference on Image Processing and Its Applications, IEE Conf. Publ. No. 307 (Michael Faraday, Stevenage, England, 1989), pp. 10–13.
  3. A. Goshtasby, G. C. Stockman, C. V. Page, “A region-based approach to digital image registration with subpixel accuracy,” IEEE Trans. Geosci. Remote Sensing GE-24, 390–399 (1980).
    [CrossRef]
  4. J. Flusser, “Adaptive method for image registration,” Pattern Recog. 25, 45–54 (1992).
    [CrossRef]
  5. A. Goshtasby, “Image registration by local approximation methods,” Image Vision Comput. 6, 255–261 (1988).
    [CrossRef]
  6. M. D. Pritt, “Automated subpixel image registration of remotely-sensed imagery,” IBM Tech. Rep. No. 85.0198 (IBM, Gaithersburg, Md., March1993).
  7. J. J. Koenderink, A. J. van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–385 (1991).
    [CrossRef] [PubMed]
  8. U. R. Dhond, J. K. Aggarwal, “Structure from stereo—a review,”IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
    [CrossRef]
  9. B. K. P. Horn, “Relative orientation,” Int. J. Comput. Vision 4, 59–78 (1990).
    [CrossRef]
  10. B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., and McGraw-Hill, New York, 1986), Chap. 13.
  11. T. S. Huang, C. H. Lee, “Motion and structure from orthographic projections,”IEEE Trans. Pattern Anal. Mach. Intell. 11, 536–540 (1989).
    [CrossRef]

1992 (1)

J. Flusser, “Adaptive method for image registration,” Pattern Recog. 25, 45–54 (1992).
[CrossRef]

1991 (1)

1990 (1)

B. K. P. Horn, “Relative orientation,” Int. J. Comput. Vision 4, 59–78 (1990).
[CrossRef]

1989 (3)

T. S. Huang, C. H. Lee, “Motion and structure from orthographic projections,”IEEE Trans. Pattern Anal. Mach. Intell. 11, 536–540 (1989).
[CrossRef]

U. R. Dhond, J. K. Aggarwal, “Structure from stereo—a review,”IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

J. Ton, A. K. Jain, “Registering Landsat images by point matching,”IEEE Trans. Geosci. Remote Sensing 27, 642–651 (1989).
[CrossRef]

1988 (1)

A. Goshtasby, “Image registration by local approximation methods,” Image Vision Comput. 6, 255–261 (1988).
[CrossRef]

1980 (1)

A. Goshtasby, G. C. Stockman, C. V. Page, “A region-based approach to digital image registration with subpixel accuracy,” IEEE Trans. Geosci. Remote Sensing GE-24, 390–399 (1980).
[CrossRef]

Aggarwal, J. K.

U. R. Dhond, J. K. Aggarwal, “Structure from stereo—a review,”IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

Dhond, U. R.

U. R. Dhond, J. K. Aggarwal, “Structure from stereo—a review,”IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

Flusser, J.

J. Flusser, “Adaptive method for image registration,” Pattern Recog. 25, 45–54 (1992).
[CrossRef]

Goshtasby, A.

A. Goshtasby, “Image registration by local approximation methods,” Image Vision Comput. 6, 255–261 (1988).
[CrossRef]

A. Goshtasby, G. C. Stockman, C. V. Page, “A region-based approach to digital image registration with subpixel accuracy,” IEEE Trans. Geosci. Remote Sensing GE-24, 390–399 (1980).
[CrossRef]

Horn, B. K. P.

B. K. P. Horn, “Relative orientation,” Int. J. Comput. Vision 4, 59–78 (1990).
[CrossRef]

B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., and McGraw-Hill, New York, 1986), Chap. 13.

Huang, T. S.

T. S. Huang, C. H. Lee, “Motion and structure from orthographic projections,”IEEE Trans. Pattern Anal. Mach. Intell. 11, 536–540 (1989).
[CrossRef]

Jain, A. K.

J. Ton, A. K. Jain, “Registering Landsat images by point matching,”IEEE Trans. Geosci. Remote Sensing 27, 642–651 (1989).
[CrossRef]

Koenderink, J. J.

Lee, C. H.

T. S. Huang, C. H. Lee, “Motion and structure from orthographic projections,”IEEE Trans. Pattern Anal. Mach. Intell. 11, 536–540 (1989).
[CrossRef]

Owczarczyk, J.

J. Owczarczyk, W. J. Welsh, S. Searby, “Performance analysis of image registration techniques,” in Third International Conference on Image Processing and Its Applications, IEE Conf. Publ. No. 307 (Michael Faraday, Stevenage, England, 1989), pp. 10–13.

Page, C. V.

A. Goshtasby, G. C. Stockman, C. V. Page, “A region-based approach to digital image registration with subpixel accuracy,” IEEE Trans. Geosci. Remote Sensing GE-24, 390–399 (1980).
[CrossRef]

Pritt, M. D.

M. D. Pritt, “Automated subpixel image registration of remotely-sensed imagery,” IBM Tech. Rep. No. 85.0198 (IBM, Gaithersburg, Md., March1993).

Searby, S.

J. Owczarczyk, W. J. Welsh, S. Searby, “Performance analysis of image registration techniques,” in Third International Conference on Image Processing and Its Applications, IEE Conf. Publ. No. 307 (Michael Faraday, Stevenage, England, 1989), pp. 10–13.

Stockman, G. C.

A. Goshtasby, G. C. Stockman, C. V. Page, “A region-based approach to digital image registration with subpixel accuracy,” IEEE Trans. Geosci. Remote Sensing GE-24, 390–399 (1980).
[CrossRef]

Ton, J.

J. Ton, A. K. Jain, “Registering Landsat images by point matching,”IEEE Trans. Geosci. Remote Sensing 27, 642–651 (1989).
[CrossRef]

van Doorn, A. J.

Welsh, W. J.

J. Owczarczyk, W. J. Welsh, S. Searby, “Performance analysis of image registration techniques,” in Third International Conference on Image Processing and Its Applications, IEE Conf. Publ. No. 307 (Michael Faraday, Stevenage, England, 1989), pp. 10–13.

IEEE Trans. Geosci. Remote Sensing (2)

J. Ton, A. K. Jain, “Registering Landsat images by point matching,”IEEE Trans. Geosci. Remote Sensing 27, 642–651 (1989).
[CrossRef]

A. Goshtasby, G. C. Stockman, C. V. Page, “A region-based approach to digital image registration with subpixel accuracy,” IEEE Trans. Geosci. Remote Sensing GE-24, 390–399 (1980).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

T. S. Huang, C. H. Lee, “Motion and structure from orthographic projections,”IEEE Trans. Pattern Anal. Mach. Intell. 11, 536–540 (1989).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

U. R. Dhond, J. K. Aggarwal, “Structure from stereo—a review,”IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

Image Vision Comput. (1)

A. Goshtasby, “Image registration by local approximation methods,” Image Vision Comput. 6, 255–261 (1988).
[CrossRef]

Int. J. Comput. Vision (1)

B. K. P. Horn, “Relative orientation,” Int. J. Comput. Vision 4, 59–78 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

Pattern Recog. (1)

J. Flusser, “Adaptive method for image registration,” Pattern Recog. 25, 45–54 (1992).
[CrossRef]

Other (3)

J. Owczarczyk, W. J. Welsh, S. Searby, “Performance analysis of image registration techniques,” in Third International Conference on Image Processing and Its Applications, IEE Conf. Publ. No. 307 (Michael Faraday, Stevenage, England, 1989), pp. 10–13.

B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., and McGraw-Hill, New York, 1986), Chap. 13.

M. D. Pritt, “Automated subpixel image registration of remotely-sensed imagery,” IBM Tech. Rep. No. 85.0198 (IBM, Gaithersburg, Md., March1993).

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Figures (4)

Fig. 1
Fig. 1

Stereo imaging system. For simplicity, the y axis points into the page, and the x axis is horizontal. Since the two imaging planes differ only in horizontal displacement, the projection P1 of a scene point to the first image lies on the same horizontal line (the epipolar line) as the projection P2 to the second image.

Fig. 2
Fig. 2

(a) Height function of a scene, (b) planar approximation of the scene, (c) scene after subtraction of the planar approximation.

Fig. 3
Fig. 3

Simulation results for a parallel projection on a 1000 × 1000 pixel image. Ten match points, shown as open squares, were projected to the computed epipolar lines. The projected points are shown as filled squares, and the true match points are shown as crosses. (Two match points are outside the field of view.)

Fig. 4
Fig. 4

The modeling error of Eq. (8) applied to the perspective projection on a 1000 × 1000 pixel image. Each curve corresponds to a different separation angle.

Tables (2)

Tables Icon

Table 1 Average Match-Point Error Reductions for Parallel Projectionsa

Tables Icon

Table 2 Average Match-Point Error Reductions for Perspective Projectionsa

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

[ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ]
f ( u , v , w ) = [ a 11 a 12 a 13 a 21 a 22 a 23 ] [ u v w ] + [ a 14 a 24 ] .
S = [ a 11 a 12 a 21 a 22 ] ,             s = [ a 13 a 23 ] ,             a = [ a 14 a 24 ] ,
f ( u , v , w ) = S [ u v ] + w s + a .
g ( u , v , w ) = T [ u v ] + w t + b ,
[ u v ] = S - 1 f ( u , v , w ) - w S - 1 s - S - 1 a ,
g ( u , v , w ) = T S - 1 f ( u , v , w ) + ( b - T S - 1 a ) + w ( t - T S - 1 s ) .
F ( x , y ) = A ( x , y ) + h ( x , y ) e ,
A ( x , y ) = T S - 1 [ x y ] + ( b - T S - 1 a ) ,
e 1 > 0 ,             e = 1 ,             h = x h = y h = 0.
[ e h ( x , y ) - l ( x , y ) ] 2 d x d y
[ x 2 x y x x y y 2 y x y 1 ] [ a b c ] = e [ x h y h h ] .
l 2 = a x l + b y l + c l = 0.
e 1 > 0 ,             e = 1 ,             i = 1 N h i = i = 1 N x i h i = i = 1 N y i h i = 0.
i = 1 N ( a 11 x i + a 12 y i + a 13 + h i e 1 - u i ) 2 + i = 1 N ( a 21 x i + a 22 y i + a 23 + h i e 2 - v i ) 2
i = 1 N ( a 11 x i 2 + a 12 x i y i + a 13 x i + e 1 x i h i - u i x i ) = 0 i = 1 N ( a 11 x i y i + a 12 y i 2 + a 13 y i + e 1 y i h i - u i y i ) = 0 i = 1 N ( a 11 x i + a 12 y i + a 13 + e 1 h i - u i ) = 0 i = 1 N ( a 21 x i 2 + a 22 x i y i + a 23 x i + e 2 x i h i - v i x i ) = 0 i = 1 N ( a 21 x i y i + a 22 y i 2 + a 23 y i + e 2 y i h i - v i y i ) = 0 i = 1 N ( a 21 x i + a 22 y i + a 23 + e 2 h i - v i ) = 0.
i = 1 N a 11 x i + a 12 y i + a 13 - u i ) 2 + i = 1 N ( a 21 x i + a 22 y i + a 23 - v i ) 2 .
i = 1 N ( e 1 h i 2 - s i h i ) = 0 ,
i = 1 N ( e 2 h i 2 - t i h i ) = 0 ,
e 1 2 h i - e 1 s i + e 2 2 h i - e 2 t i = 0 ,             i = 1 N .
h i = s i e 1 + t i e 2 .
m = [ α + σ ( α 2 + 4 ) 1 / 2 ] / 2 ,
[ 1 / ( 1 + m 2 ) 1 / 2 , m / ( 1 + m 2 ) 1 / 2 ] .
1 - ( 1 / 2 π ) 0 2 π cos θ d θ = 1 - 2 / π 36 % ,

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