Method and system for the calibration of an object reconstruction device

A calibration system for calibrating an object reconstruction device, comprising:

• a) a plurality of C cameras (Cam) adapted for image acquisition, a j-th camera of the plurality of cameras (Cam) being identified as Camj for all j=1 . . . C, comprising:
• a sensor with a sensitive area formed by pixels for capturing an image, and
• an optic, with an optical axis with orientation vector ({right arrow over (OJ) )} for establishing a focus on the sensor and a portion of a space projected on the sensor, and
• the plurality of cameras (Cam) being spatially distributed in positions of a closed surface (S) defining an observation region (R) therein, where the cameras (Cam) are configured for having the orientation vector ({right arrow over (OJ)}) of their optical axes oriented towards a pre-established point (P) of the observation region (R);
• characterized in that the object reconstruction device (1) further comprises:
• b) a calibration solid comprising a number (NB) of balls (BL), with NB greater than or equal to one, the k-th ball being identified as BLk for all k=1 . . . NB and wherein if two or more balls are used they have different diameters;
• c) at least one positioning mechanism of the calibration solid configured for positioning said calibration solid in the observation region (R);
• d) computational equipment in communication with the at least one positioning mechanism and with the plurality of cameras (Cam) and configured for:
• causing in the plurality of cameras (Cam) the capture of images of the observation region (R) when the at least one positioning mechanism positions the calibration solid in said observation region (R), and
• receiving the images acquired by the plurality of cameras (Cam);
• wherein the computational equipment is configured to:
• (1) capture data of the object reconstruction device comprising the following sub-steps:
• for each of the cameras (Camj), provide their intrinsic parameters and estimated values of at least the following extrinsic calibration parameters:
• orientation {right arrow over ((OJ))} in the observation region (R) within the closed surface (S) and
• position of an optical center (cj) being also the point on the optical axis of the optics where all rays passing through it remain unrefracted;
• establish, based on the intrinsic and extrinsic parameters, a bijective correspondence (fj) between each coordinate of a pixel (px) of the image captured by the sensor of the camera (Camj) and the set of coordinates of the points of the epipolar line (r) of the space, which passes through the optical center (cj) of the camera (Camj) and are projected by the optic of the camera (Camj) in that same pixel (px) after the image capture;
• perform a predetermined number (N) of experiments (E), the i-th experiment being identified as Ei for all i=1 . . . N, according to the following sub-steps:
• the positioning mechanism positioning the calibration solid in the observation region (R) at a different position;
• activating the plurality of cameras (Cam) for each of them (Camj) to capture an image of the calibration solid positioned in the observation region (R);
• receiving the images (Iij) acquired by the cameras (Cam), where in each image (Iij) each of the balls (BLk) captured in the image is shown as connected regions (BPkij) of pixels, where index i with i=1 . . . N denotes the experiment number, index j denotes the camera which has captured the image (Iij) with j=1 . . . C, and k denotes the ball (BL) from among the balls of the calibration solid with k=1 . . . NB,
• (2) post-process the captured data comprising the following sub-steps:
• going through the set of captured images (Iij), where for each captured image (Iij) the following sub-steps are carried out:
• identify the connected regions (BPkij) of pixels corresponding to a specific ball (BLk) of the calibration solid, if it appears in the image Iij;
• for each connected region (BPkij) of a ball (BLk) of the calibration solid that does appear in an image (Iij), determine:
• a pixel (pxijk) corresponding to the center of said connected region (BPkij) in the image (Iij);
• and
• in the space within the closed surface, determining a normalized direction vector (dijk) of an epipolar line (rijk) which corresponds to the pixel (pxijk) through correspondence (fj);
• determine the points of the space (pik′) which minimize the summation of distances to the epipolar lines (rijk) defined by a directions (dijk) of each ball (BLk) in each experiment (Ei):
• 𝓅
• ik
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• =
• [
• ∑
• j
• =
• 1
• C
• [
• I
• -
• d
• ijk
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• d
• ijk
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• ]
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• 1
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• where I is the identity matrix and where T denotes the transposition of the vector dijk;
• for each camera (Camj), determine the extrinsic calibration parameters such that the correspondence (fj) between the epipolar line defined between the center (cj) and the point (pik′), and the pixel (pxijk), for any experiment (Ei) and for any ball (BLk) is satisfied.

A non-transitory computer-readable medium comprising instructions which, when run by a computational equipment, causes the computational equipment to:

• (1) capture data of the object reconstruction device comprising the following sub-steps:
• for each of the cameras (Camj), provide their intrinsic parameters and estimated values of at least the following extrinsic calibration parameters:
• orientation ({right arrow over (OJ))} in the observation region (R) within the closed surface (S) and
• position of an optical center (cj) being also the point on the optical axis of the optics where all rays passing through it remain unrefracted;
• establish, based on the intrinsic and extrinsic parameters, a bijective correspondence (fj) between each coordinate of a pixel (px) of the image captured by the sensor of the camera (Camj) and the set of coordinates of the points of the epipolar line (r) of the space, which passes through the optical center (cj) of the camera (Camj) and are projected by the optic of the camera (Camj) in that same pixel px after the image capture;
• perform a predetermined number (N) of experiments (E), the i-th experiment being identified as Ei for all i=1 . . . N, according to the following sub-steps:
• the positioning mechanism positioning the calibration solid in the observation region (R) at a different position;
• activating the plurality of cameras (Cam) for each of them (Camj) to capture an image of the calibration solid positioned in the observation region (R);
• receiving the images (Iij) acquired by the cameras (Cam), where in each image (Iij) each of the balls (BLk) captured in the image is shown as connected regions (BPkij) of pixels, where index i with i=1 . . . N denotes the experiment number, index j denotes the camera which has captured the image/i with j=1 . . . C, and k denotes the ball (BL) from among the balls of the calibration solid with k=1 . . . NB,
• (2) post-process the captured data comprising the following sub-steps:
• going through the set of captured images (Iij), where for each captured image (Iij) the following sub-steps are carried out:
• identify the connected regions (BPkij) of pixels corresponding to a specific ball (BLk) of the calibration solid, if it appears in the image (Iij);
• for each connected region (BPkij) of a ball (BLk) of the calibration solid that does appear in an image (Iij), determine:
• a pixel (pxijk) corresponding to the center of said connected region (BPkij) in the image (Iij);
• and
• in the space within the closed surface, determining a normalized direction vector (dijk) of an epipolar line (rijk) which corresponds to the pixel (pxijk) through correspondence (fj);
• determine the points of the space (pik′) which minimize the summation of distances to the epipolar lines (rijk) defined by a directions (dijk) of each ball (BLk) in each experiment (Ei):
• 𝓅
• ik
• ′
• =
• [
• ∑
• j
• =
• 1
• C
• [
• I
• -
• d
• ijk
• ⁢
• d
• ijk
• T
• ]
• ]
• -
• 1
• ⁢
• ∑
• j
• =
• 1
• C
• [
• I
• -
• d
• ijk
• ⁢
• d
• ijk
• T
• ]
• ⁢
• c
• j
• where I is the identity matrix and where T denotes the transposition of the vector (dijk);
• for each camera (Camj), determine the extrinsic calibration parameters such that the correspondence (fj) between the epipolar line defined between the center (cj) and the point (pik′), and the pixel (pxijk), for any experiment (Ei) and for any ball (BLk) is satisfied.