Condition Number-Based Smoothins of Optical Flow Fields

This invention relates generally to the field of image processing, and more particularly to an improved method and apparatus for indicating motion.

As image processing technology has advanced, so has the number of applications for the technology. In particular, image processing systems have proved extremely useful in moving object indication applications.

In the field of moving object indication, sequential images from a sensor can be analyzed to create an optical flow field. See, e.g., "Determining Optical Flow", B. K. P. Horn and B. G. Schunck, Computer Vision, p. 185, North-Holland Publishing, 1981. This optical flow field is an array of vectors indicating the magnitude and direction of movement on a pixel by pixel basis. The optical flow field can then be used to indicate motion or to track a moving object, for example, for purposes of targeting or security monitoring. Other uses of the optical flow field include sensor motion estimation, terrain structure estimation, and autonomous navigation.

Because of noise introduced in acquiring images, errors often exist in the optical flow vectors generated for a given object. For example, if the optical flow vectors corresponding to an object moving across the image plane of an image sensor should be equal at any given point in time, noise introduced by the image sensor could result in non-equal optical flow vectors corresponding to the object. To minimize these errors, smoothing operations are performed on the optical flow vectors. See, e.g., "Image Flow: Fundamentals and Algorithms", B. G. Schunck, Motion Understanding--Robot and Human Vision, Chapter 2, Kluwer Academic Publishers, 1988.

Present imaging systems rely on "guesses" made by a human operator to determine certain factors involved in minimizing errors in optical flow fields. Therefore, a need has arisen for a system that performs error minimization (smoothing) based upon the image, rather than on ad hoc determinations by the user of the system.

In accordance with the present invention, a method and apparatus for image processing is provided which substantially eliminates or reduces disadvantages and problems associated with prior systems for processing images. Image signals are generated using an image sensor and transmitted to an optical flow field generator. The optical flow field generator generates a smooth optical flow field and stores the smooth optical flow field in a memory. The optical flow field generator smooths the optical flow field by generating a condition number for each optical flow vector in the optical flow field and then minimizing the sum of the lack of accuracy and the product of the condition number and lack of smoothness for each optical flow vector. The stored, smooth optical flow field may be processed to indicate or track motion.

An important technical advantage of the present invention inheres in the fact that the optical flow field is smoothed based on a condition number generated for each of the optical flow vectors. The condition number is used as a weighting factor to improve smoothing processing of the optical flow field.

For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawing wherein:

FIG. 1 illustrates a block diagram of an image processing system constructed according to the teachings of the present invention;

FIG. 2 illustrates detection of terrain or object shape according to one embodiment of the present invention; and FIG. 3 illustrates in more detail Optical Flow Field Generator of FIG. 1.

FIG. 1 illustrates a block diagram of an imaging system 10 constructed according to the teachings of the present invention. An image sensor 12 is used to sense images and generate image signals to be processed. Image sensor 12 may comprise any one of a number of image sensors. For example, image sensor 12 may comprise forward looking infrared sensors or visible light TV sensors. More than one image sensor can be used with the present invention to provide additional information on the images to be processed. As shown in FIG. 1, image sensor 14 may be used in parallel with image sensor 12. With this additional sensor, two channels of image data are available for processing. Image sensors 12 and 14 may or may not be the same type of image sensor. For example, image sensor 12 may be a forward looking infrared sensor and image sensor 14 may be a green light sensor.

The image signals generated by optical sensors 12 and 14 are transmitted by transmission circuitry 13, such as output drivers, to optical flow field generator 16. Optical flow field generator 16 generates an optical flow field for the images sensed by sensors 12 and 14. The optical flow vector associated with each pixel of image data may be represented as

wherein O.sub.ij is the optical flow vector for a pixel located at row i in column j, and u.sub.ij is the magnitude in the x direction of the optical flow vector for the pixel located at row i in column j, v.sub.ij is the magnitude in the y direction of the optical flow vector for the pixel located at row i in column j, and x and y are unit vectors in the x and y directions, respectively. For any pixel, the values for u and v are computed from the following equations

A, B, C, D, E, and F are functions of image intensity. Where two image sensors are provided, such as image sensors 12 and 14 of FIG. 1, A, B, C, D, E, and F may comprise first order derivatives of the image intensity of a given pixel. A, B, and C are calculated with respect to the image signal from one sensor, e.g., image sensor 12, such that A is the first order derivative of the image intensity of a given pixel with respect to x, B is the first order derivative of the image intensity with respect to y, and C is the first order derivative of the image intensity with respect to time. D, E, and F are calculated with respect to the image signal for a separate sensor, e.g., image sensor 14, such that D is the first order derivative of the image intensity with respect to the x direction, E is the first order derivative of the image intensity with respect to the y direction, and F is the first order derivative of the image intensity with respect to time.

If only one image sensor is used, then A, B, C, D, E, and F are second order derivatives. In such a case, A is the second order derivative of the image intensity with respect to x and x, B is the second order derivative of the image intensity with respect to x and y, C is the second order derivative of the image intensity with respect to x and t, D is the second order derivative of the image intensity with respect to y and x, E is the second order derivative of the image intensity with respect to y and y, and F is the second order derivative of the image intensity with respect to y and t. In all of above cases, x and y are spatial coordinates representing the conventional x and y directions on an x-y axis and t represents time. It should be understood that more than two sensors can be used to provide signals for generating optical flow vectors without departing from the teachings of the present invention. For examples of the derivations of Equations 2 and 3, see, e.g., "Determining Optical Flow", B. K. P. Horn and B. G. Schunck, Computer Vision, p. 185, North Holland Publishing, 1981; "Multispectral Constraints for Optical Flow Computation", V. Markandey and B. E. Flinchbaugh, Proc. Third Intl. Conf. on Computer Vision, p. 38, 1990; and "Constraints for the Computation of Optical Flow", F. Girosi, A. Verri, and V. Torre, Proc. Workshop on Visual Motion, IEEE, p. 116, 1989.

Equations 2 and 3 can be solved for u and v provided that the matrix ##EQU1## is non-singular. It can be shown that the condition number of matrix E is

where .parallel.E.parallel. is the square root of the largest eigenvalue of E.sup.T E.

The condition number, c, provides a confidence measure for each optical flow vector that may be used in smoothing the optical flow field. Flow field smoothing is performed by minimizing a weighted sum of two terms, where the first term, e.sub.s, is a measure of the lack of smoothness of the flow field, and the second term, e.sub.c, is a measure of the lack of accuracy. The two terms, e.sub.s and e.sub.c, may be represented by the following formulas. ##EQU2## where u.sub.x and u.sub.y are partial deriatives of u with respect to spacial coordinates x and y, and v.sub.x and v.sub.y are partial derivatives of v with respect to spacial coordinations x and y. The magnitude of the initial flow vector calculated according to formulas 2 and 3 in the x and y directions are u and v, respectively.

Smoothing is performed by minimizing the weighted sum of Equations 6 and 7, as given by Equation 8 below: ##EQU3## where c(x.sub.c,y.sub.c) is the central pixel in the area of summation. It can be shown that Equation 8 may be minimized using the following iterative equations: ##EQU4## where n is the number of iterations. As can be seen from Equation 8, the condition number of the E matrix for a given pixel is multiplied by the measure of the lack of smoothness at that pixel as a weighting factor. Use of the condition number as a weighting factor in Equation 8 provides for a weighting factor that is based on the image signal rather than ad hoc determinations by the user of the image processing system.

Use of Equations 9 and 10 to calculate the optical flow vectors for an optical flow field provides an improved smoothing technique for image analysis systems performing motion indication or analogous functions.

According to one embodiment of the present invention shown in FIG. 3, before using the smoothing functions of Equations 9 and 10, a median filter 31 can be used to eliminate noise spikes from the original optical flow vectors calculated according to Equations 2 and 3. Such a median filter could be a 3.times.3 spatial extent median filter, although filters of other sizes may also be used. The optical flow vectors resulting from such median filters could then be smoothed according to Equations 9 and 10.

The condition number-based optical flow field smoothing described above can be implemented on a general purpose computer capable of converting the video signals to digital values and then performing the smoothing processing. In the alternative, a dedicated microprocessor based system or application specific integrated circuit could be used to perform the condition number-based smoothing described above.

The number of iterations of Equations 9 and 10 performed depends on the requirements of imaging system 10. The number of iterations of Equations 9 and 10 could be determined by the speed of the system performing the optical flow field generation. For example, if each pixel is to be smoothed 30 times a second, the number of iterations may depend upon the length of time required by optical flow field generator 16 to perform the smoothing operation for a particular pixel. As another example, since each iteration of Equations 9 and 10 reduces the error expressed in Equation 7, iterations of equations 9 and 10 may be stopped when the rate of error reduction with successive iterations becomes insignificantly small, as in the case of asymptotic convergence, or if the error actually starts increasing with successive iterations after reaching a minima point.

Once the optical flow field has been generated by optical flow field generator 16, the optical flow field is stored in a memory 18. Memory 18 may comprise, for example, a random access memory. The form of the data stored in memory 18 may be in the form of a two-dimensional array, wherein the magnitude in both the x and the y directions of the optical flow vectors for each pixel are stored. The magnitudes in the x and y direction for each optical flow field vector may be real numbers.

Memory 18 is accessed by analyzer 20. Analyzer 20, in general, processes the optical flow field stored in memory 18 for the purpose required by imaging system 10, and may comprise a microprocessor based system operating to determine motion based on the magnitude and direction of the vectors making up the optical flow field. In particular, analyzer 20 may comprise a moving target indication system, in which information on moving targets may be provided through monitor 22 to an operator of imaging system 10. It should be recognized that monitor 22 shown in FIG. 1 is for purposes of example only, and could be another type of output device, such as a printer or other device designed to operate in response to a given type of movement. Another example of analyzer 20 is a robust tracking system, in which moving objects are tracked, for example, for targeting purposes.

According to one embodiment of the present invention, analyzer 20 may comprise a terrain structure or object shape processor. FIG. 2 illustrates one embodiment of the operation of terrain or object shape detection by sensor motion. As shown in FIG. 2, a sensor 24 is moved in a known pattern, resulting in changes in the relative position of an object 26 with respect to sensor 24. This change in relative position is equivalent to motion, and the shape of the object (or the terrain structure) can be detected by analyzing the optical flow fields generated during sensor movement. In this way, three-dimensional terrain structures or object shapes may be measured, and representations of these shapes or structures, such as maps, may be created. Another technique by which object shape may be estimated is by analyzing intensity changes caused by lighting changes.

It should be understood that "motion indication", as used herein, describes both motion of objects and sensor motion, and thus includes the example of three-dimensional representation generation. Moreover, since the teachings herein relate to image intensity, "motion indication" also includes detection of intensity or shading changes.

In summary, an imaging system is provided in which image signals generated by image sensors are processed and optical flow vectors are produced. These optical flow vectors are further processed by a condition number-based smoothing operation. These smoothed optical flow vectors are then accessed to provide information, such as motion or terrain structure information, on the image sensed by the image sensors.

Although the present invention has been described in detail, it should be understood that various changes, substitutions and alterations can be made without departing from the spirit and scope of the invention as defined by the appended claims.