Volume 33 #1

Contents

1. Analysis of sexual partner preferences in Eurydema ornata and E. oleracea in free choice context
2. Optimal affine approximation of image projective transformation
3. Recognition of projectively transformed planar figures XII. On new methods for projectively-invariant description of ovals in composition with a linear element of a plane
4. Edge detection based mobile robot indoor localization
5. Robust criterion for vanishing point estimation of linear trajectories of detected vehicles in a video stream
6. Matching SAR and optical images by independed referencing to a vector map
7. Increase of computational efficiency of projective image transformation on SIMD-architectures
8. Comparison of the classifying and similarity metric-based neural networks through the recognition of the filed “gender” in Russian Federation passport
9. Heartbeat-evoked responses on EEG in slow wave sleep in cats
10. Polysomnographic study of central sleep apnea in cats

Replacing the projective transformation with a substantially simpler affine transformation occurs in many areas of technical vision. At the same time, the concept of accuracy of an affine approximation of a projective transformation is not formalized in the literature. This, in turn, leads to the absence of problem statements and theoretically sound methods for affine approximation of the projective transformation. This work aims to eliminate this gap. The authors proposed to use the root mean square (RMS) and the maximum pointwise discrepancy in the transformed image coordinates system as criteria for the accuracy of the affine approximation of projective transformation. Based on these criteria, the problem of finding the optimal affine approximations is formulated. The convexity of the obtained optimization problems is proved. A method for image transformation, using optimal affine approximations to save computational resources, is proposed.

Key words: homography, homography estimation accuracy, transformation affine approximation, linearization, convex analysis

DOI: 10.1134/S0235009219010062

References:

• Balickij A.M., Savchik A.V., Gafarov R.F., Konovalenko I.A. O proektivno invariantnyh tochkah ovala s vydelennoj vneshnej prjamoj [On projectively invariant points of an oval with a distinguished outer straight line] Problemy peredachi informacii [Problems of Information Transmission]. 2017. V. 53 (3). P. 84–89 (in Russian).
• Berezskij O.N., Berezskaja K.M. Kolichestvennaja ocenka kachestva segmentacii izobrazhenij na osnove metric [Quantitative assessment of the quality of image segmentation based on metrics] Upravljajushhie sistemy i mashiny [Control systems and machines]. 2015. № 6. P. 59–65 (in Russian).
• Bolotova Ju.A., Spicyn V.G., Osina P.M. Obzor algoritmov detektirovanija tekstovyh oblastej na izobrazhenijah i videozapisjah [An overview of the algorithms for detecting text areas in images and video recordings] Komp’juternaja optika [Computer optics]. 2017. V. 41 (3) (in Russian).
• Efimov A.I., Novikov A.I. Algoritm pojetapnogo utochnenija proektivnogo preobrazovanija dlja sovmeshhenija izobrazhenij [Algorithm of phased refinement of projective transformation for image combining] Komp’juternaja optika [Computer optics]. 2016. V. 40 (2) (in Russian).
• Konovalenko I.A., Shemjakina Ju.A. Analiz velichin oshibki pri netochnom proektivnom preobrazovanii chetyrehugol’nika [Error values analysis for inaccurate projective transformation of a quadrangle]. Informacionnye tehnologii i nanotehnologii [information technology and nanotechnology]. 2018. P. 1251–1260 (in Russian).
• Nikolaev P.P. Proektivno invariantnoe opisanie neploskih gladkih figur. 1. Predvaritel’nyj analiz zadachi [Projectively invariant description of non-planar smooth figures. 1. Preliminary analysis of the problem] Sensornye sistemy [Sensory sysytems]. 2016. V. 30 (4). P. 290–311 (in Russian).
• Pritula N.E., Nikolaev P.P., Sheshkus A.V. Sravnenie dvuh algoritmov proektivno-invariantnogo raspoznavanija ploskih zamknutyh konturov s edinstvennoj vognutost’ju [Comparison of two algorithms of projectively invariant recognition of flat closed contours with a single concavity] Informacionnye tehnologii i sistemy-2014 [Information technologies and systems-2014], Almanac. ISBN 978-5-901158-25-8 С. 367–373 P. 367–373 (in Russian).
• Savchik A.V., Nikolaev P.P. Teorema o peresechenii T-i Hpoljar [The Theorem of T- and H- Polars Intersections Count] Informacionnye process [Information processes]. 2016. V. 16(4). P. 430–443 (in Russian).
• Holopov I. S. Algoritm korrekcii proektivnyh iskazhenij pri malovysotnoj s#jomke [Algorithm for the correction of projective distortion in low-altitude shooting] Komp’juternaja optika [Computer optics]. 2017. V. 41 (2) (in Russian).
• Chernov T.S., Il’in D.A., Bezmaternyh P.V., Faradzhev I.A., Karpenko S.M. Issledovanie metodov segmentacii izobrazhenij tekstovyh blokov dokumentov s pomoshh’ju algoritmov strukturnogo analiza i mashinnogo obuchenija [Study of methods for segmentation of images of text blocks of documents using algorithms for structural analysis and machine learning] Vestnik Rossijskogo fonda fundamental’nyh issledovanij [Vestnik RFFI]. 2016. № 4. P. 55–71 (in Russian).
• Shemjakina Ju. A. Ispol’zovanie tochek i prjamyh dlja vychislenija proektivnogo preobrazovanija po dvum izobrazhenijam ploskogo ob’ekta [Using points and lines to calculate the projective transformation from two images of a flat object] Informacionnye tehnologii i vychislitel’nye sistemy [information technology and computing systems]. 2017. No. 3. P. 79–91. (in Russian).
• Shemjakina Ju. A., Zhukovskij A. E., Faradzhev I. A. Issledovanie algoritmov vychislenija proektivnogo preobrazovanija v zadache navedenija na planarnyj ob’ekt po osobym tochkam [The Research of the Algorithms of a Projective Transformation Calculation in the Problem of Planar Object Targeting by Feature Points] Iskusstvennyj intellekt i prinjatie reshenij [Artificial intelligence and decision making]. 2017. No. 1. P. 43–49 (in Russian).
• Alter T. 3D pose from 3 corresponding points under weakperspective projection. Technical report, Massachusetts inst. of tech. cambridge artificial intelligence lab, 1992.
• Aradhye H., Myers G. Method and apparatus for recognition of symbols in images of three-dimensional scenes, US Patent 7,738,706. 2010.
• Baltzopoulos V. A videofluoroscopy method for optical distortion correction and measurement of knee-joint kinematics. Clinical Biomechanics. 1995. V. 10 (2). P. 85–92.
• Chen H., Sukthankar R., Wallace G., Li K. Scalable alignment of large-format multi-projector displays using camera homography trees. Proceedings of the conference on Visualization’02. 2002. P. 339–346.
• Darko P., Volker S., Leif K. Interactive image completion with perspective correction. The Visual Computer. 2006. V. 22 (9–11). P. 671–681.
• Dong-Gyu S., Oh-Kyu K., Rae-Hong P. Object matching algorithms using robust hausdorff distance measures. IEEE Transactions on image processing. 1999. V. 8 (3). P. 425–429.
• Dubuisson M., Jain A. A modified hausdorff distance for object matching. Proceedings of the 12th IAPR International Conference.1994. V. 1. P. 566–568.
• Faugeras O. What can be seen in three dimensions with an uncalibrated stereo rig? European conference on computer vision. 1992. P. 563–578.
• Fréchet M. Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Matematico di Palermo (1884–1940). 1906. V. 22 (1). P. 1–72.
• Gruen A. Adaptive least squares correlation: a powerful image matching technique. South African Journal of Photogrammetry, Remote Sensing and Cartography. 1985. V. 14 (3). P. 175–187.
• Heckbert P. Fundamentals of texture mapping and image warping. 1989. UC Berkeley Master’s thesis. 86 p.
• Hsu S., Sawhney H. Influence of global constraints and lens distortion on pose and appearance recovery from a purely rotating camera. Applications of Computer Vision, 1998. WACV’98. Proceedings., Fourth IEEE Workshop. 1998. P. 154–159.
• Huang J., Singh A., Ahuja N. Single image super-resolution from transformed self-exemplars. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2015. P. 5197–5206.
• Huttenlocher D., Klanderman G., Rucklidge W. Comparing images using the hausdorff distance. IEEE Transactions on pattern analysis and machine intelligence. 1993. V. 15 (9). P. 850–863.
• Jaccard P. Étude comparative de la distribution florale dans une portion des alpes et des jura. Bull Soc Vaudoise Sci Nat. 1901. V. 37. P. 547–579.
• Jesorsky O., Kirchberg K.J., Frischholz R.W. Robust face detection using the hausdorff distance. International Conference on Audio-and Video-Based Biometric Person Authentication. 2001. P. 90–95.
• Kadir T., Zisserman A., Brady M. An affine invariant salient region detector. European conference on computer vision. 2004. P. 228–241.
• Karpenko S., Konovalenko I., Miller A., Miller B., Nikolaev D. UAV control on the basis of 3d landmark bearing-only observations. Sensors. 2015. V. 15 (12). P. 29802–29820.
• Kutulakos K.N., Vallino J. Affine object representations for calibration-free augmented reality. Virtual Reality Annual International Symposium, 1996., Proceedings of the IEEE. 1996. P. 25–36.
• Lorenz H., Döllner J. Real-time piecewise perspective projections. GRAPP. 2009. P. 147–155.
• Mallon J., Whelan P.F. Projective rectification from the fundamental matrix. Image and Vision Computing. 2005. V. 23 (7). P. 643–650.
• Mikolajczyk K., Schmid C. An affine invariant interest point detector. European conference on computer vision. 2002. P. 128–142.
• Mikolajczyk K., Schmid C. Scale & affine invariant interest point detectors. International journal of computer vision. 2004. V. 60 (1). P. 63–86.
• Morel J-M., Yu G. Asift: A new framework for fully affine invariant image comparison. SIAM journal on imaging sciences. 2009. V. 2 (2). P. 438–469.
• Orrite C., Herrero J.E. Shape matching of partially occluded curves invariant under projective transformation. Computer Vision and Image Understanding. 2004. V. 93 (1). P. 34–64.
• Povolotskiy M.A., Kuznetsova E.G., Khanipov T.M. Russian license plate segmentation based on dynamic time warping. 31st European Conference on Modelling and Simulation (ECMS). 2017. P. 285–291.
• Skoryukina N., Chernov T., Bulatov K., Nikolaev D.P., Arlazarov V. Snapscreen: Tv-stream frame search with projectively distorted and noisy query. Ninth International Conference on Machine Vision. 2017. V. 10341. P. 103410Y.
• Skoryukina N., Shemiakina J., Arlazarov V., Faradjev I. Document localization algorithms based on feature points and straight lines. Tenth International Conference on Machine Vision. 2018. V. 10696. P. 106961H.
• Stein G.P. Lens distortion calibration using point correspondences. Computer Vision and Pattern Recognition. Proceedings. IEEE Computer Society Conference. 1997. P. 602–608.
• Tu-ichi O., Kiyoshi M., Toshiyuki S. Obtaining surface orientation from texels under perspective projection. IJCAI. 1981. P. 746–751.
• Wei H., Wang Y., Forman G., Zhu Y. Map matching by fréchet distance and global weight optimization. Technical Paper, Departement of Computer Science and Engineering. 2013. P. 19.
• Zhukovsky A.E., Arlazarov V.V., Postnikov V.V., Krivtsov V.E. Segments graph-based approach for smartphone document capture. Eighth International Conference on Machine Vision . 2015. V. 9875. P. 98750P.
• Zwicker M., Räsänen J., Botsch M., Dachsbacher C., Pauly M. Perspective accurate splatting. Proceedings of Graphics interface 2004. 2004. P. 247–254.