How LumiScan X Works

The camera array consists of 13 monochrome cameras with 1.2 MPix and 12 bit each (Sensor Technical Specifications). The cameras observe the same measurement volume from different positions; their relative positions and orientations define the angular sampling of the system. Because the viewpoints are physically separated, every scene point appears with parallax between the camera images, and this parallax provides the geometric information for depth estimation.

In the LumiScan Viewer, the Frame tab shows the images of the 13 individual cameras, and Capture Center View exports the image of the center camera (see User Interface and Data Export). LumiScan X is available with three opening angles: 60°, 40° and 30° (Opening angle).

LumiScan X is a passive 3D camera: unlike structured-light or laser triangulation systems, it does not fundamentally require a projected light pattern to determine the geometry of a scene, but derives the depth from the images of its cameras. It does need enough image information for correspondence estimation, however, so depending on the application, suitable ambient or application-specific illumination is necessary.

For surfaces without texture, the pattern projector LumiScan SL projects a pattern onto the surface: an artificial texture that makes it possible to find correspondences. The Trigger Out signal of LumiScan X triggers the LumiScan SL simultaneously with the image acquisition (Trigger Out Signal).

Each camera can be described by a calibrated perspective projection model, provided that this is an adequate approximation of its optics. A point \(\mathbf{X}\) in the reference coordinate system is transformed into the coordinate system of camera \(i\):

Here \(R_i\) is the rotation matrix and \(\mathbf{t}_i\) the translation vector of camera \(i\), and \(\mathbf{X}_{c,i}\) is the point in camera coordinates. The point is then projected into the image with the intrinsic camera matrix \(K_i\). In homogeneous coordinates, the ideal pinhole projection onto the image point \((x_i, y_i)\) is:

where \(\lambda_i\) is a scale factor. Lens distortion is modeled separately. With these parameters, every image observation can be related to a ray in a common three-dimensional coordinate system.

The intrinsic parameters describe the optical properties of an individual camera: the focal lengths, the principal point and the lens distortion parameters. They determine how a point in space is projected onto the image sensor (\(K_i\) and the distortion model in Image Formation Model).

The extrinsic parameters describe the position and orientation of each camera relative to a common coordinate system: a three-dimensional translation and a three-dimensional rotation (\(\mathbf{t}_i\) and \(R_i\)). Together with the intrinsic parameters, they define the geometry of the complete camera array.

Calibration errors act directly on the reconstructed 3D points: small errors in the orientation, position or focal length of a camera can cause systematic depth deviations. A camera array therefore needs a mechanically stable construction and an accurate calibration, and changes to the optical configuration or to the relative camera geometry can make a recalibration necessary.

The calibration file (.hdvcal) of LumiScan X contains the intrinsic and extrinsic parameters of all 13 cameras:

For details, see Calibration and FAQ: Where are the calibration files and which one do I need?.

The first task is to find corresponding image locations across the viewpoints. A surface point appears at different pixel coordinates in each camera, and correspondence algorithms identify these observations from the image content. In a calibrated system, epipolar geometry restricts the search: for two cameras, the point that corresponds to a point in the first image must lie on a known line in the second image, the epipolar line. This reduces the search space for matching. The reconstruction of LumiScan X uses this epipolar constraint between its calibrated cameras.

With more than two viewpoints, a scene point can be observed by several cameras, and each observation adds a geometric constraint. The three-dimensional position can be estimated by minimizing the deviation between the projected point and its observations. A common formulation is:

The reconstruction can produce different representations of the scene. A depth map assigns a distance to each image location; a point cloud is a set of reconstructed three-dimensional points in a coordinate system. LumiScan X computes depth maps with a resolution of 1.2 MP (1280 × 960) and a 3D point throughput of 7.2 million points per second. The LumiScan Viewer displays the result as a point cloud. Its coordinate system is the one output by LumiScan X: the camera is at the origin and aligned in the direction of the Z axis, and the unit is meters.

Further processing removes invalid measurements, evaluates confidence or extracts geometric features. In the LumiScan Viewer:

The quality of a three-dimensional measurement cannot be described by a single resolution or accuracy value. The following properties must be distinguished:

These properties are related but not interchangeable. A depth map can contain many pixels and still show considerable uncertainty in their depth values, and a system can repeat its measurements very well and still have systematic geometric errors. For this reason, the specifications of LumiScan X state the point-to-point distance, the calibration accuracy and the temporal Z noise as separate values, each for a 1 m edge measurement field (Key values of LumiScan X); none of them can be read as the absolute accuracy of any measurement. Evaluate accuracy, precision, spatial resolution and measurement conditions separately.

Depth sensitivity depends on the baseline between the viewpoints (Baseline and Depth Sensitivity). For a given baseline, the disparity becomes smaller with increasing distance, so the depth estimation becomes more sensitive to small correspondence errors. A longer baseline improves the geometric depth sensitivity, but increases the perspective differences between the cameras, which can make it more difficult to find corresponding features, especially on objects with complex geometry.

A camera array contains several camera pairs with different relative positions and therefore different baselines. Shorter baselines give smaller perspective differences, which can simplify correspondence; longer baselines give more parallax and can improve depth sensitivity where reliable correspondences are available. The reconstruction of LumiScan X uses several baselines of its camera array and combines their information, which balances these properties.

Each camera of LumiScan X records a conventional image at its native sensor resolution: unlike a microlens-based plenoptic camera, the array does not divide the pixels of one sensor among several angular samples. The number of reconstructed depth values does not, however, indicate the smallest geometric feature that can be resolved. Spatial resolution is influenced by:

The size of a pixel projected onto the object grows with the distance: a detail that is resolved at a short working distance may no longer be distinguishable at a larger one. Evaluate the achievable resolution for the intended measurement configuration.

A single camera records only the surfaces that are visible from its viewpoint. A multi-view system observes the scene from several directions, so a surface that is hidden from one camera can remain visible from another. Consider an object with a recess: from one viewpoint, the side wall hides part of the bottom; from another viewpoint, this part is visible. By evaluating the observations of several cameras, a light field camera can reconstruct more of the scene geometry than a single camera. Surfaces that are hidden from every viewpoint cannot be reconstructed without additional assumptions, so how far occlusions are reduced depends on the actual visibility and the camera geometry.

The spacing of the viewpoints determines the angular information: closely spaced viewpoints give small changes of perspective, widely spaced viewpoints more geometric diversity. A light field camera has to balance the density of its angular sampling against the required baseline, the field of view and robust correspondence.

Industrial machine vision frequently meets surfaces that are difficult to measure: metallic and polished components, dark materials, objects with weak texture, fine structures and complex geometries with recesses or occlusions.

The working distance is the distance between the camera and the measured object; the measurement volume is the region in which a reliable three-dimensional reconstruction is possible. Both depend on the optical configuration. For a given field of view, the observed area grows with the distance while the projected size of a feature decreases, and the depth sensitivity changes as well. Choosing the working distance is therefore a compromise between measurement volume, spatial resolution, depth sensitivity, visibility and optical configuration: short working distances favor high geometric detail, while large objects or robot work spaces may require longer ones.

With LumiScan X, optimum results are achieved at measuring distances of 250 - 3000 mm and measurement volumes of 200 - 3360 mm, depending on the configuration. Each standard configuration defines the focus, the standard calibration range and the field of view at the minimum and maximum working distance (Standard Configurations). Select the configuration according to the requirements of the application, and set Depth Range to the actual position of the measurement object.

A reconstructed point cloud is an estimate of the visible scene geometry, not a validated measurement. Individual points can carry uncertainty from the calibration, the correspondence, optical effects or the surface properties. For industrial measurement tasks, evaluate the results against known reference objects or geometries. Depending on the application, validation can include:

Enable Capture Statistics in the LumiScan Viewer shows the valid points and the valid ratio of a capture (Data Export). Document the resulting performance together with the measurement conditions, particularly when 3D data is used for dimensional inspection, robot positioning or automated quality decisions.