December 9, 2014Computer Vision Lecture 23: Motion Analysis 1 Now we will talk about… Motion Analysis

December 9, 2014Computer Vision Lecture 23: Motion Analysis 2 Motion analysis Motion analysis is dealing with three main groups of motion- related problems: Motion detection Moving object detection and location. Derivation of 3D object properties. Motion analysis and object tracking combine two separate but inter-related components: Localization and representation of the object of interest (target). Trajectory filtering and data association. One or the other may be more important based on the nature of the motion application.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 3 Motion analysis

December 9, 2014Computer Vision Lecture 23: Motion Analysis 4 Differential Motion Analysis A simple method for motion detection is the subtraction of two or more images in a given image sequence. Usually, this method results in a difference image d(i, j), in which non-zero values indicate areas with motion. For given images f 1 and f 2, d(i, j) can be computed as follows: d(i, j) = 0 if | f 1 (i, j) – f 2 (i, j) |   = 1 otherwise

December 9, 2014Computer Vision Lecture 23: Motion Analysis 5 Differential Motion Analysis

December 9, 2014Computer Vision Lecture 23: Motion Analysis 6 Difference Pictures Another example of a difference picture that indicates the motion of objects (  = 25).

December 9, 2014Computer Vision Lecture 23: Motion Analysis 7 Difference Pictures Applying a size filter (size 10) to remove noise from a difference picture.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 8 Difference Pictures The differential method can rather easily be “tricked”. Here, the indicated changes were induced by changes in the illumination instead of object or camera motion (again,  = 25).

December 9, 2014Computer Vision Lecture 23: Motion Analysis 9 Differential Motion Analysis In order to determine the direction of motion, we can compute the cumulative difference image for a sequence f 1, …, f n of more than two images: Here, f 1 is used as the reference image, and the weight coefficients a k can be used to give greater weight to more recent frames and thereby highlight the current object positions.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 10 Cumulative Difference Image Example: Sequence of 4 images: a 2 = a 3 = 2a 4 = 4 Result:

December 9, 2014Computer Vision Lecture 23: Motion Analysis 11 Differential Motion Analysis Generally speaking, while differential motion analysis is well-suited for motion detection, it is not ideal for the analysis of motion characteristics.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 12 Optical flow Optical flow reflects the image changes due to motion during a time interval dt which must be short enough to guarantee small inter-frame motion changes. The optical flow field is the velocity field that represents the three-dimensional motion of object points across a two- dimensional image. Optical flow computation is based on two assumptions: The observed brightness of any object point is constant over time. Nearby points in the image plane move in a similar manner (the velocity smoothness constraint).

December 9, 2014Computer Vision Lecture 23: Motion Analysis 13 Optical flow

December 9, 2014Computer Vision Lecture 23: Motion Analysis 14 Optical Flow The basic idea underlying most algorithms for optical flow computation: Regard image sequence as three-dimensional (x, y, t) space Determine x- and y-slopes of equal-brightness pixels along t-axis The computation of actual 3D gradients is usually quite complex and requires substantial computational power for real-time applications.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 15 Optical Flow Let us consider the two-dimensional case (one spatial dimension x and the temporal dimension t), with an object moving to the right: x t

December 9, 2014Computer Vision Lecture 23: Motion Analysis 16 Optical Flow Instead of using the gradient methods, one can simply determine those straight lines with a minimum of variation (standard deviation) in intensity along them: x t Flow undefined in these areas

December 9, 2014Computer Vision Lecture 23: Motion Analysis 17 Optical flow Optical flow computation will be in error if the constant brightness and velocity smoothness assumptions are violated. In real imagery, their violation is quite common. Typically, the optical flow changes dramatically in highly textured regions, around moving boundaries, at depth discontinuities, etc. Resulting errors propagate across the entire optical flow solution.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 18 Optical flow Global error propagation is the biggest problem of global optical flow computation schemes, and local optical flow estimation helps overcome the difficulties. However, local flow estimation can introduce large errors for homogeneous areas, i.e., regions of constant intensity. One solution of this problem is to assign confidence values to local flow estimations and consider those when integrating local and global optical flow.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 19 Optical flow

December 9, 2014Computer Vision Lecture 23: Motion Analysis 20 Optical flow

December 9, 2014Computer Vision Lecture 23: Motion Analysis 21 Detecting Motion Pattern in Optical Flow Fields We can compute the local speed gradient to detect certain basic motion patterns. The speed gradient is defined as the direction of the steepest speed increase, regardless of the direction of motion.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 22 Detecting Motion Pattern in Optical Flow Fields There are four different basic motion patterns: counterclockwise and clockwise rotation, contraction, and expansion. They can be combined to form spiral motion. counterclockwiseclockwisecontractionexpansion movement speed gradient Idea: A consistent angle between the direction of movement and the orientation of the speed gradient indicates a specific motion pattern.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 23 Detecting Motion Pattern in Optical Flow Fields direction of movement orientation of speed gradient Angles other than 0, 90, 180, and 270 degrees correspond to spiral motion patterns.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 24 Feature Point Correspondence Feature point correspondence is another method for motion field construction. Velocity vectors are determined only for corresponding feature points. Object motion parameters can be derived from computed motion field vectors. Motion assumptions can help to localize moving objects. Frequently used assumptions include, like discussed above: Maximum velocity Small acceleration Common motion

December 9, 2014Computer Vision Lecture 23: Motion Analysis 25 Feature Point Correspondence The idea is to find significant points (interest points, feature points) in all images of the sequence—points least similar to their surroundings, representing object corners, borders, or any other characteristic features in an image that can be tracked over time. Basically the same measures as for stereo matching can be used. Point detection is followed by a matching procedure, which looks for correspondences between these points in time. The main difference to stereo matching is that now we cannot simply search along an epipolar line, but the search area is defined by our motion assumptions. The process results in a sparse velocity field. Motion detection based on correspondence works even for relatively long interframe time intervals.

December 9, 2014Computer Vision Lecture 23: Motion Analysis 26 Feature Point Correspondence

December 9, 2014Computer Vision Lecture 23: Motion Analysis 27 And this is… The End