Abstract: A calibration mark apparatus includes a support having at least one wall with at least one calibration pattern on the least one wall and at least one attachment portion extending from the least one wall. The attachment portion may be a flap extending from at least one wall for attaching the support to a surface or a net. The support may be a three-dimensional (3D) structure. The calibration mark apparatus may have walls that are foldable along a common edge into a single plane. The calibration mark apparatus may have a base connecting the walls including raised tab portions arranged to fit into slots in the flap. The flap may include openings for attaching multiple supports together by a rope that is arranged to feed through the openings. The calibration mark apparatus may include a bracket to mount the support to a surface or a net by clips.

Abstract: A method for calibrating a camera without the decomposition of camera parameters into extrinsic and intrinsic components is provided. Further, there is provided a method for tracking an object in motion comprising capturing one or more image frames of an object in motion, using one or more calibrated cameras that have been calibrated according to a calibration method that generates and uses a respective transformation matrix for mapping three-dimensional (3D) real world model features to corresponding two-dimensional (2D) image features. The tracking method further comprises determining, using a hardware processor, motion characteristics of the object in motion based on the captured one or more image frames from each one or more calibrated cameras, the determining of the motion characteristics based on implicit intrinsic camera parameters and implicit extrinsic camera parameters of the respective transformation matrix from each respective one or more calibrated cameras.

Abstract: A calibration mark apparatus includes a support having at least one wall with at least one calibration pattern on the least one wall and at least one attachment portion extending from the least one wall. The attachment portion may be a flap extending from at least one wall for attaching the support to a surface or a net. The support may be a three-dimensional (3D) structure. The calibration mark apparatus may have walls that are foldable along a common edge into a single plane. The calibration mark apparatus may have a base connecting the walls including raised tab portions arranged to fit into slots in the flap. The flap may include openings for attaching multiple supports together by a rope that is arranged to feed through the openings. The calibration mark apparatus may include a bracket to mount the support to a surface or a net by clips.

Abstract: Embodiments are disclosed for determining the spin rate and the spin axis of a ball in flight. In some embodiments, a method comprises: capturing, with an image sensor, a time series of images of a ball in flight and corresponding image capture times; inputting, with at least one processor, the image frames and the image capture times into a machine learning model; and predicting, with the at least one processor, a spin axis and a spin rate of the ball based on the machine learning model.

Abstract: In a first step, a time series of images are resized to a smaller dimension, and the smaller images are fed into a first classifier that is trained to classify as a ball any objects in the smaller images that resemble a ball. In a second step, the smaller images are mapped back to the series of images, and regions in the series of images that contain the mapped ball are cropped from the series of images. The mapped ball is shifted based on a velocity of the mapped ball in the cropped regions, and the second classifier regresses center coordinates and a radius of the shifted ball, classifies whether the shifted ball is the ball based on a confidence score, and updates the shifted ball in the cropped regions based on the regressed center coordinates and radius.

Abstract: Template points associated with a template are obtained. An image of the template is captured using a camera. The template points of the template are mapped to image points in the image of the template to determine a 2-dimensional transformation matrix (H2D). Pose transform is obtained based on an initial projection matrix resulting from a prior calibration of the camera and the 2-dimensional transformation matrix (H2D), the pose transform having an incomplete rotation matrix. The pose transform is normalized to obtain an updated pose transform having a complete rotation matrix. An affine transform is applied using the complete rotation matrix and a translation vector of the normalized pose transform to the initial projection matrix to obtain an updated projection matrix.

Abstract: An image of an object is received, the image being captured by a camera. Two-dimensional (2D) image points on perimeters of the object in the image are determined. Using a rotation component of a homography matrix, the 2D image points are converted into corresponding three-dimensional (3D) points on a 3D conic section that passes through a center of the camera and the perimeters of the object. The 3D points on the 3D conic section are normalized. A principal direction to a center of the object is determined, based on the normalized 3D points on the 3D conic section. 2D object center is determined based on the principal direction and the rotation component of the homography matrix.

Abstract: A method may include collecting first and second image data of an object motion, the first and second image data respectively including first and second frames captured by a first and a second camera. The method may include identifying an object included in the first and second frames and modeling two-dimensional pose estimations of the object for each identified frame. The two-dimensional pose estimations may indicate coordinate positions of the object features that contribute to the object motion. The method may include generating a first and a second three-dimensional joint heatmap corresponding to the object identified in the first and second frames based on features indicated in the two-dimensional pose estimations. The method may include determining a time delay between the first and second cameras based on the three-dimensional joint heatmaps and generating a motion journal that summarizes the motion associated with the object based on the time delay.

Abstract: Embodiments are disclosed for determining a spin rate and axis of a ball using deep learning. In some embodiments, a method comprises: training a deep learning network on training images of spinning balls, each spinning ball having at least one feature point in a time series that forms a two-dimensional (2D) ellipse image in a 2D plane; capturing, with at least one camera, a series of images of a ball; predicting, with the trained deep learning network, spin measurements associated with the ball based on the series of images; determining a spin rate of the ball based on the spin measurements; determining coefficients of a 2D ellipse model based on the spin measurements and the spin rate; and determining, with the at least one processor, a spin axis of the ball in 3D space based on the 2D ellipse model and the spin rate.

Abstract: Disclosed are embodiments for determining the position and speed of a projectile in three-dimensional world coordinates using a single camera and radar. In some embodiments, a method comprises: determining a zero radial speed time of the projectile based on radar measurements of the projectile; determining a radial speed of the projectile at a particular time based on the radar measurements; determining a radial speed slope at the particular time based on the radial speed measurements; determining a two-dimensional image point of the projectile at the particular time; determining a depth scale coefficient at the particular time based on the zero radial speed time, the radial speed, the radial speed slope, the image point, and a homographic transformation; and determining a position of the projectile in space at the particular time based on a three-dimensional position of the camera, the depth scale coefficient, the image point and the homographic transformation.

Abstract: Disclosed are embodiments for determining the position and speed of a projectile in 3D world coordinates using a calibrated camera and radar. In some embodiments, a method comprises: capturing a sequential set of images of a projectile in motion; determining a radial velocity of the projectile; determining a set of two-dimensional (2D) image points representing respective locations of the projectile in the sequential set of images; determining respective depths of the 2D image points in their respective 2D image planes based on the 2D image points, time intervals between the captured 2D images, the radial velocity and a rotational part of a homographic transformation, the homographic transformation configured to project three-dimensional (3D) world coordinates to the 2D image planes; and determining a set of 3D world points of the projectile in the 3D world coordinates based on the 2D image points, the respective depths thereof and the homographic projection.

Abstract: A spin-estimation system may include an image-capturing sensor positioned and configured to capture images of an object within a field of view of the image-capturing sensor. The spin-estimation system may be configured to perform one or more operations to analyze spin properties of the object. The operations may include setting an image capture framerate that corresponds to a minimum spin motion of the object, printing an orientation marker on an outer surface of the object, and capturing, by the image-capturing sensor at the set image capture framerate, images of the object after starting motion of the object. The operations may include isolating the object in each image to generate isolated object images. The operations may include generating an object marker segmentation map based on the isolated object images. A spin rate and a spin axis may be estimated based on the object marker segmentation map using deep learning approaches.

Abstract: A method includes receiving motion data of a user in an environment with respect to a plurality of instances of a first action by the user, determining a kinematic movement based on receiving the motion data, analyzing the kinematic movement using a neural network, obtaining a plurality of outcome types with respect to the first action of the user, correlating the kinematic movement with the at least one indication of the outcome type with respect to the first action, classifying an outcome of the first action as at least one of the plurality of outcome types, determining which of the kinematic movements of the user result in the at least one of the plurality of outcome types, and providing instructions to the user to alter the determined kinematic movements of the user that result in the at least one of the plurality of outcome types.

Abstract: An image taken of an object in motion is received. At least three markers on the object in motion in the image are detected. Image points of the three markers are determined. Based on the image points of the three markers, depths of the object in motion at the image points are determined, where the depths are determined relative to an image plane of the image. Using the image points and the depths, three-dimensional (3D) world points representing a position of the object in motion in a 3D real world coordinate are determined.

Abstract: A method for calibrating a camera without the decomposition of camera parameters into extrinsic and intrinsic components is provided. Further, there is provided a method for tracking an object in motion comprising capturing one or more image frames of an object in motion, using one or more calibrated cameras that have been calibrated according to a calibration method that generates and uses a respective transformation matrix for mapping three-dimensional (3D) real world model features to corresponding two-dimensional (2D) image features. The tracking method further comprises determining, using a hardware processor, motion characteristics of the object in motion based on the captured one or more image frames from each one or more calibrated cameras, the determining of the motion characteristics based on implicit intrinsic camera parameters and implicit extrinsic camera parameters of the respective transformation matrix from each respective one or more calibrated cameras.

Abstract: Automatic club recognition during a golf swing is provided. At least one processor receives a series of images of a golf club captured during a golf swing. At least one processor detects from the series of images one or more sticker labels placed on the golf club. At least one processor classifies a golf club type of the golf club based on recognizing a marker, e.g., a unique or particular marker, coded on the one or more sticker labels, the marker for representing a specific type of golf club.

Abstract: A calibration mark apparatus includes a support having at least one wall with at least one calibration pattern on the least one wall and at least one attachment portion extending from the least one wall. The attachment portion may be a flap extending from at least one wall for attaching the support to a surface or a net. The support may be a three-dimensional (3D) structure. The calibration mark apparatus may have walls that are foldable along a common edge into a single plane. The calibration mark apparatus may have a base connecting the walls including raised tab portions arranged to fit into slots in the flap. The flap may include openings for attaching multiple supports together by a rope that is arranged to feed through the openings. The calibration mark apparatus may include a bracket to mount the support to a surface or a net by clips.

Abstract: A method may include collecting first and second image data of an object motion, the first and second image data respectively including first and second frames captured by a first and a second camera. The method may include identifying an object included in the first and second frames and modeling two-dimensional pose estimations of the object for each identified frame. The two-dimensional pose estimations may indicate coordinate positions of the object features that contribute to the object motion. The method may include generating a first and a second three-dimensional joint heatmap corresponding to the object identified in the first and second frames based on features indicated in the two-dimensional pose estimations. The method may include determining a time delay between the first and second cameras based on the three-dimensional joint heatmaps and generating a motion journal that summarizes the motion associated with the object based on the time delay.