A Practical Camera Calibration System on Mobile Phones

Transcription

1 Advanced Science and echnolog Letters Vol.7 (Culture and Contents echnolog 0), pp A Practical Camera Calibration Sstem on Mobile Phones Lu Bo, aegkeun hangbo Department of Computer Science, Gachon Universit, Sujung-Gu, Songnam, Kunggi-Do, Korea lubo0@hotmail.com, tkwhangbo@gachon.ac.kr Abstract. e propose a practical camera calibration sstem on mobile phones to calibrate the camera s intrinsic parameters, based on the geometrical propert of the vanishing points. his sstem onl requires the camera to observe a rectangular card shown in a few (at least four) different orientations. he experimental results of real images show that the proposed calibration sstem is robust, simple, and practicable. Kewords: Camera Calibration, Vanishing Point, k-means, Line detection Introduction Camera calibration is a valuable process in the field of computer vision. ith the development of the mobile phones, there has been extensive research into the technolog of AR in mobile phones in recent ears. Owing to these developments, it is necessar to develop a calibration sstem that is suitable for mobile phones. In general, camera calibration techniques can be divided into three categories: the traditional method, the method based on the active vision technique, and the camera self-calibration method. he traditional method [] requires an accurate threedimensional or two-dimensional calibration target; the method based on the active vision method [], a particular movement of the camera is necessar, and a relativel high accurac of experimental equipment is required; the camera self-calibration method makes use of the self-constraints of the camera for calibration. his method can further be divided into the technique based on Kruppa s equations [], and that of the absolute quadric method [], both of which can work without a reference calibration target. Both these methods require high computational complexit. herefore, particularl in low-performance mobile phones, the process is extremel time-consuming. In our sstem, in order to avoid such high computational complexit, we implement a camera calibration method based on the geometrical properties of the vanishing points that are determined b two perpendicular groups of parallel lines [5]. he vanishing points can be obtained from an arbitrar rectangular card, which can be a card used in everda life (e.g., credit card, business card) and is therefore eas to obtain. In comparison with other methods, our method is robust, eas to use, and requires less computation. ISSN: 87- ASL Copright 0 SERSC

2 Advanced Science and echnolog Letters Vol.7 (Culture and Contents echnolog 0) Related ork he pinhole camera model is a widel used model in the field of computer vision. Let the image point p( υ, ν), which is located in the image coordinate frame, be the projection of the three-dimensional point P (x,, z ) located in the world coordinate frame. hen, the projection equation can be written as: z c f υ d x ν 0 0 s f d 0 c x x c R z K R x z () here K is the intrinsic parameters matrix of the camera, and R and are the rotation matrix and translation matrix, respectivel. In the intrinsic parameters matrix K, ƒ is the camera's focal length, d x, d are the CCD/CMOS sensor pixel's length and width, respectivel, (c, c is the principal point, and s is a factor accounting for the x ) skew due to non-rectangular. Fig.. Geometr model of the ideal projection of two perpendicular groups of parallel lines A set of parallel lines in the three-dimensional world is projected onto a set of converging lines in the image plane; these lines converge at a common point known as the vanishing point. he line that joins the camera center and the vanishing point of the parallel lines in the world is parallel to these parallel lines. If there are two perpendicular groups of parallel lines in the world, as illustrated in Fig., then: L // L, L // L, L L ; L and L 's projection l, l intersect at vanishing point A in image plane Ω, and L, and L 's projection l, l intersect at vanishing point B. Based on the propert of the vanishing point, it is known that the lines joining the optical center O and the vanishing points A and B are parallel to the Copright 0 SERSC 7

3 Advanced Science and echnolog Letters Vol.7 (Culture and Contents echnolog 0) respective lines corresponding to these in the world: OA // L, OB // L, then, OA OB, and O is on a sphere with a diameter of AB. e conclude that, if two perpendicular groups of parallel lines exist, the optical center O is on the sphere of which the diameter is the line joining the two vanishing points obtained b those parallel lines. Proposed calibration algorithm for mobile platform. Pre-processing he first step in this stage is Gaussian smoothing, for reducing the noise that is generated b camera's sensor, as well as reducing bad lighting conditions to a certain extent. Following this, we enhance the edge details of the image b increasing the global contrast b means of Histogram equalization; however, as this ma increase the contrast of background noise, in the third step, we again use Gaussian filtering again to minimize the little edge's influence. hereafter, we detect the edge using the Cann algorithm, and finall, we detect the lines b means of Hough lines detection.. Vanishing point detection In this stage, we use the k-means algorithm to classif the lines into four groups, based on the line's angle and intercept. hereafter, we compute the average line of each line group. In the last step, we use the average lines to calculate the vanishing points.. Camera calibration based on vanishing points In the image coordinate frame, the vanishing point coordinates obtained b the projection of the parallel lines are A( υ A, ν A ), B( υ B, ν B ). hen, the vanishing point coordinates in the camera coordinate frame are: A(( υ A - c x )d x,(ν A - c )d, f), B(( υ B - c x )d x,(ν B - c )d, f) he equation of the sphere of which the diameter is AB : υ A υ B ν A ν B x d x c x d x d c d υ A υ B ν A ν B z f d x d () Based on the conclusion of section, the optical center with a diameter of AB, and therefore, we substitute O(0,0,0) O(0,0,0) is on the sphere into equation (), then: 8 Copright 0 SERSC

4 Advanced Science and echnolog Letters Vol.7 (Culture and Contents echnolog 0) υ A υ B ν A ν B d x c x d x d c d υ A υ B ν A ν B f d x d () Simplifing equation (): (c υ )(c υ ) (c x A x B f x ν A )(c f ν B ) 0 () Equation () is a function of the intrinsic camera parameters (f x, f, c x, c ) and has four unknowns. It is necessar to obtain at least four images (each rectangular card image get vanishing points) from different orientations In Hun's method [5], the lens distortion coefficient is considered, and a non-linear optimization based on Nelder- Mead simplex algorithm is used to optimize the intrinsic parameters. Because the distortion of a mobile camera lens is ver small, we used the method of least squares to solve the intrinsic parameters. Experiments e took four images, shown in Fig., using the rear camera of a Galax Note moving it around a card so that different vanishing points could be obtained. he calibration results of the images in Fig. s are listed in able s data. In order to evaluate our method objectivel, we also tested two other image data sets obtained from the same device and the results are shown in able. e used Zhang's chessboard method [] to calibrate the camera as a reference. In this test, each test data set is obtained b capturing the chessboard in 0 different orientations using the same device(fig. ). hree data sets were tested, and the results are shown in able. hen we compare the results of our sstem with the results of Zhang's method, there are no significant differences between two; however, our sstem is more flexible. Fig.. est image sample (he image resolution is 80 60) Fig.. Chessboard image data set used for Zhang s method Copright 0 SERSC 9

5 Advanced Science and echnolog Letters Vol.7 (Culture and Contents echnolog 0) able. Results of calibration based on vanishing points able. Results of Zhang's Method Camera parameter focal length principle point f x 58 f 5 c x c 7 Data Data Data Camera parameter f x focal length principle point f c x c Data Data Data Conclusion In this paper, in accordance with the low computing performance of mobile phones, we have presented a camera calibration sstem with low computational complexit. his sstem can be used to obtain the vanishing points in the image of an arbitrar rectangular card and to calibrate the intrinsic camera parameters based on these vanishing points. Our experiments show that this sstem is flexible and effective. References. Zhan Z., A flexible new technique for camera calibration, IEEE ransactions on Pattern Analsis and Machine Intelligence, Vol., No., pp 0-, Ma S. D., A self-calibration technique for active vision sstems, IEEE rans. Robot. Automat, vol., no., pp Faugeras O. D., Luong Q., Mabank S.: Camera self-calibration: heor and experiments. In Proc. ECCV, LNCS 588, pp., Springer Verlag, (99).. riggs B., Autocalibration and the absolute quadric, Proc. IEEE Conf. Computer Vision, Pattern Recognition, pp , (997). 5. Huo J., Yang., Yang M.: A self-calibration technique based on the geometr propert of the vanish point. Acta Optica Sinica, vol. 0, no., pp. 65-7, (00). 0 Copright 0 SERSC