Device for calibrating omnidirectional mirrors

Description of the invention

The subject of the invention is a device for calibrating omnidirectional mirrors for use in the calibration of catadioptric systems used in particular for recording lightning discharges, as well as in the medical and military industries.

Omnidirectional image recording is widely used in many fields of science, technology, and industry, including photography, medicine, the military, and cartography. Many applications, in addition to the typical omnidirectional image information obtained using an optical recorder aimed directly at an omnidirectional mirror, also require the ability to transform the image from 3D space to a 2D panoramic image—so-called 3D-to-2D projection. Another common need is to determine the properties of objects in three-dimensional space based on images acquired in an omnidirectional system. The solution to both problems is the calibration of a so-called catadioptric system, a system composed of an image recorder and an omnidirectional mirror, forming a single optical system. Calibration is a process that allows for the direct correlation of individual omnidirectional image pixel positions seen on the recorder's matrix with the scalable coordinates of the observed 3D space. This enables, among other things, subsequent determination of an object's geometric dimensions, velocity, and acceleration at a known distance from the mirror-camera system.

The process of calibrating an omnidirectional system, where the image is wide-angle, is typically an extremely complex mathematical procedure. This is due to significant nonlinearities in the calibration function required, which depend on the omnidirectional scattering of light rays reflected from the mirror. For mirror curvatures described by simple mathematical functions, the calibration process requires slightly less computational power. It should be noted, however, that in both cases, the influence of the nonlinearity of the optical recorder lens itself is also a significant element. Currently, there are techniques that allow for the accurate determination and compensation of optical recorder nonlinearity: Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on pattern analysis and machine intelligence, 22(11), 1330-1334. Calibration techniques can be divided into two groups: calibration systems for classical optical systems consisting solely of a recorder with a narrow-angle lens, the so-called pinhole camera, and for optical systems of recorders with a wide-angle lens, such as a fisheye lens or catadioptric recorder-omnidirectional mirror systems, commonly referred to as fisheye cameras. For the calibration of pinhole cameras, one of the most commonly used techniques is: Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on pattern analysis and machine intelligence, 22(11), 1330-1334. For fisheye camera calibration systems, a different procedure is commonly used: Scaramuzza, D., Martinelfi, A., & Siegwart, R. (2006, January). A flexible technique for accurate omnidirectional camera calibration and structure from motion. In Fourth IEEE International Conference on Computer Vision Systems (ICVS'06) (pp. 45-45). IEEE improved by Urban, S., Leitloff, J., & Hinz, S. (2015). Improved wide-angle, fisheye and omnidirectional camera calibration. ISPRS Journal of Photogrammetry and Remote Sensing, 108, 72-79.

Patent literature provides solutions for the calibration of omnidirectional mirrors, which focus primarily on the analytical determination of mirror parameters with typical curvatures such as a parabola (US 2003004694 A1) or a hyperbola (CN 100469137-C, US 6744569-B2). Solutions dedicated to the calibration of conical mirrors (CN 106558081 A) are also known, in which the catadioptric camera-mirror system is not axially symmetric.

More universal methods for calibrating omnidirectional mirrors of any type are also known. This group includes the invention known from patent application CN 101354790 A, which presents a method for obtaining a panoramic image based on a 3D/2D transformation using the Taylor series model. Another example of a similar procedure is disclosed in patent application US 2008002023 A1, in which calibration is obtained using the so-called Zemax model combined with a homographic transformation and an affine transformation. Also noteworthy is the solution known from the application description CN 103268610 A, in which calibration consisting in finding the coefficients of the polynomial function describing the 3D/2D projection is performed using the Levenberg-Marquardt method used as a tool to minimize the calibration error.

Chinese patent application CN 115170671 A discloses a device for calibrating an optical system, comprising a ring-shaped measurement module and a cylindrical reference module. The ring-shaped measurement module is located at one end of the connecting cylinder near the camera, and a square through-hole is located in the center of the ring-shaped measurement module. The cylindrical reference module contains a light source at one end and a reflecting mirror at the other.

In known solutions, image distortion is determined for the mirror curvature, thus ignoring distortions resulting from, among other things, shape and dimensional errors. Furthermore, known solutions are often dedicated to a specific type of omnidirectional mirror and typically require mirror calibration each time the optical recorder is changed.

A device for calibrating omnidirectional mirrors, comprising an optical recorder, a cylindrical body and a holder for an omnidirectional mirror, according to the invention, is characterized in that the holder for an omnidirectional mirror is located in the axis of the cylindrical body, wherein both the holder and the cylindrical body are connected to the base, and the body is connected to the base in a rotatable manner and the holder is connected to the base in a fixed manner, and furthermore the body comprises a viewing hole at one of its ends, and the optical recorder is located on the side of this viewing hole and is directed with its lens towards the holder, and its optical axis is located coaxially with respect to the axis of the cylindrical body and with respect to its axis of rotation, wherein inside the body on its inner surface there is a replaceable calibration template coaxial with respect to the cylindrical body.

Advantageously, the body comprises a first cover at one end and a second cover at the other, wherein the first cover is rotatably connected to the base via a precision bearing, and the second cover located opposite it comprises a viewing hole, and between the first cover and the second cover the body comprises rods arranged at an equal distance from the axis of rotation of the body and parallel to it, wherein the rods are connected to the first cover at one end and to the second cover at the other, and the template is on the inside of these bars.

Further advantages are obtained if the handle is in the form of a threaded pin located in the axis of rotation of a cylindrical body fixedly connected to the base, on which a lock nut is screwed, and the first cover has a through hole in the axis of rotation of the body, and the pin protrudes through this hole in the first cover into the interior of the body.

Further benefits are obtained if the viewing hole is in the second cover.

Further advantages are obtained if each lid has a flange on its periphery, protruding towards the lid located opposite, and on its surface on the side of the lid located opposite, each lid has a circular groove, coaxial with respect to the axis of rotation of the body, and the connection of the ends of the rods with the lids is between the groove and the flange, and the grooves of the first lid and the second lid have the same diameter, with the parallel edges of the template being embedded in these grooves.

Further benefits are obtained if it includes two sets of tensioning lugs and the template is releasably connected to the lid flanges by these tensioning lugs.

The solution according to the invention allows for the rapid positioning of the omnidirectional mirror relative to the calibration template and the optical axis of the recorder, and its application is not limited to a specific type of mirror. The invention enables the determination of coefficients that determine the characteristics of the mirror's projection from the 3D system onto the 2D image of the recorder matrix, as well as the correction of the lens's radial and axial distortion. The resulting function allows for the association of individual points in 3D space with specific pixels on the optical recorder matrix. Based on the coefficients describing the 3D/2D projection in an omnidirectional system, the mirror's curvature, describing its shape, can be determined. The device allows for the determination of image deformation independently at any point on the mirror's surface, not solely relative to its curvature. To achieve this, a successive series of images of the omnidirectional mirror is recorded. Subsequent images must be recorded for a series of different calibration template positions relative to the rotation axis aligned with the optical axis of the omnidirectional mirror. Numerical analysis allows us to determine which parts of the mirror distort the image the most. Combined with the determined mirror projection characteristics, this allows for the determination of image projection errors both in the recorder's 2D matrix and in 3D space. Furthermore, it allows for subsequent correction of deformations introduced by the catadioptric system. Individual calibration parameters characterizing both the optical recorder and the mirror itself can be determined at various stages of calibration. This makes it easier to use the mirror in cooperation with other types of optical recorders without the need to calibrate it each time.

The device for calibrating omnidirectional mirrors, in an example embodiment, is explained in more detail in the drawing, where Fig. 1 shows the device in cross-section along the axis of rotation of the body; Fig. 2 - schematically selects the dimensions of the device body for a given omnidirectional mirror.

PL 249097 BI

The device for calibrating omnidirectional mirrors, according to the invention, in the embodiment example comprises a base 1 which has a mounting sleeve 2 perpendicular to it. In the mounting sleeve 2, at its axis, a threaded pin 3 is fixedly connected to it, and on the circumference of this sleeve 2 a base 4 is mounted via a precision bearing 5 with the possibility of adjusting the axial clearance. A cylindrical body 6 is connected to the base 4, which comprises a first cover 7 and a second cover 8 parallel to it, which are connected to each other by means of rods 9 evenly spaced at an equal distance from the spindle 3, and thus from the axis of rotation of the cylindrical body 6. The rods 9 are connected to the first cover 7 at one end and to the second cover 8 at the other. On the surfaces of the covers 7 and 8 facing each other, on their periphery directly next to the rods 9, from the inside of the body 6, each of the covers 7 and 8 has a circular groove 10, coaxial with respect to the axis of rotation of the body 6. Each of these grooves 10 has the same diameter. The first cover 7 is on the side of the base 1 and is connected to the base 4, and the second cover 8 located opposite it has a through viewing hole 11 located in the axis of rotation of the body 6. Opposite the viewing hole 11, on the side opposite the tube, there is an optical recorder 12, the lens 13 of which is turned towards the viewing hole 11 and is positioned with its optical axis in the axis of rotation of the body 6. Each of the covers 7 and 8 has a flange 14 located on the outside of the body 6 and facing the cover 7 or 8 situated opposite it. Inside the body 6 there are two sets of tensioning handles 15, one of which is on the side of the first cover 7 and the other on the side of the second cover 8, wherein the tensioning handles 15 of one of the sets are connected by tensioning screws 16 to the flange of the first cover 7, and the tensioning handles 15 of the second set are connected by tensioning screws 16 to the flange 14 of the second cover 8. Each of the sets of tensioning handles 15 contains eight tensioning handles 15. Each groove 10 is between the tensioning handles 15 and the rods 9. In the grooves 10 there are mounted parallel edges of a replaceable calibration template 17 in the form of a rectangular rigid flexible paper sheet, tangential to the inner surface of the body 6 coaxial to its axis of rotation, on the inner surface of which a calibration pattern is applied. The recorder 12 is mounted on a tripod 18 connected to the base 1. The pin 3 constitutes a holder 3' for an omnidirectional mirror 19 having a threaded hole in its optical axis, and a locking nut 20 is screwed onto the pin 3. The rods 9 are screwed to the covers 7, 8 with mounting screws 21. The base 1 has mounting holes 22 allowing it to be screwed to a given surface, such as a worktop.

The principles of operation of the invention are described below.

The device is selected based on the basic parameters of the omnidirectional mirror 19, including the diameter of the smaller base dm, the diameter of the larger base D_m, minimum reflection angle and maximum reflection angle Inner diameter D_ct of the body 6 must be at least 1.1 times the diameter of the larger base D_m omnidirectional mirror 19.

D_ct > l,lD_m (1)

The internal height of the body 6 measured between the tensioning handles 15 connected to the collar 14 of the first cover 7 and the tensioning handles 15 connected to the collar 14 of the second cover 8 depends on the height H_m omnidirectional mirror 19, its minimum angle of reflection jSmin, maximum angle of reflection β^_ΒΧ and from the internal diameter of the body 6.

H_cc >H_m + Ιαη(β_Mη) + tanf_max) (2)

First, an omnidirectional mirror 19 is screwed onto the mandrel 3, which has a central threaded through hole in its optical axis, and the position of the omnidirectional mirror 19 is stabilized by a locking nut 20. A template 17 is placed in the grooves 10 of the covers 7 and 8 and its position is stabilized by means of tensioning handles 15, by screwing the tensioning handles 15 to the flanges 14, by means of tensioning screws 16 which pass through the through holes in the template 17 situated at its parallel edges on the side of the first covers 7 and the second covers 8. The recorder 12 is positioned with the optical axis of its lens 13 in the optical axis of the omnidirectional mirror 19 and thus in the axis of rotation of the body 6. The body 6 is rotated and an image containing a 3D/2D projection of a specially developed calibration template 17 placed symmetrically on the inner surface of the cylindrical body 6 is recorded. The images are collected in the full range of the rotation angle a_c has a beneficial effect on the compensation of image deformations resulting from the imperfections in the manufacturing of the template 17 itself and its positioning in the device body 6. The effects observed for ac=<0°,180°> are largely compensated by taking into account in the analysis images from the angle range ac=<180°,360°>.