Rapsodo Pte. Ltd.

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 (H 2D ). Pose transform is obtained based on an initial projection matrix resulting from a prior calibration of the camera and the 2-dimensional transformation matrix (H 2D ), 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.

Embodiments are disclosed for determining a ball impact location on a surface of a striking object. In some embodiments, a method comprises: capturing a series of images including at least three images of a striking object prior to impact with a stationary ball; determining, based on center coordinates of surfaces of the striking object captured in the at least three images, a circumference of a circle; shifting the ball along the circumference of the circle to a virtual position such that the ball at the virtual position is in contact with a first surface of the striking object; determining a first impact location on the first surface of the striking object in contact with the shifted ball at the virtual position.

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.

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.

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.

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.

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.

Embodiments are disclosed for object detection using deep learning. In some embodiments, a method comprises: extracting, with a machine learning model, a first region from an image; pooling, with the machine learning model, the first region to a second region that is smaller than the first region; predicting, with the machine learning model, a geometric center and radius of a blob of pixels in the second region and a confidence score associated with the predicting; and classifying, with the machine learning model, the blob of pixels as a ball based on the confidence score.

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.

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.