A special-purpose convolution filter was developed that converts a printed target composed of black and white squares into a pattern of dots. The output image consists of mostly a black background and a pattern of white dots, corresponding to the intersection points of the black and white squares. The result is an output image that requires less processing than the original input image of black and white squares against an unknown background. Printed targets are much easier to fabricate than other types of targets since they can be created and modified with a computer drawing utility and a standard office printer.

The Block Convolution Mask (BCM) filter transforms a printed target into a set of pinpoints that can in theory be single pixel points. The uniqueness of this innovation is the ability to minimize dimensional error associated with imaging a target for positioning or measurement applications.

BCM can be defined as a type of image gradient operator or edge detection filter. Most gradient operators and edge detection filters are square arrays (or filter masks) of size N x N where N is an odd number. The BCM described herein is also a square N x N filter mask, where N is now even.

By imaging targets, information can be obtained from a two-dimensional (2-D) camera image, thus providing the x, y, z position of the target in the camera coordinate system. The formulas that transform a 2-D image to 3-D position x, y, z are based on a pinhole camera model (figure 1), where m and n are pixel locations (integer values) in the x and y image direction; L_x and L_y are the physical dimension of the target (or distance between targets) in the x and y direction; s_x, s_y, and s are "scale factors" in the x and y direction and the RMS value; m₀ and n₀ are the center x and y location of the target in the image; m_cand n_c are the pixel locations of the center of the image; and is a value that must be determined by calibration of the camera/lens system. Note that f is the focal length of the lens.

Figure 1. Position Formulas Based on Pinhole Camera Model

Applications for the printed target and convolution filter include those calling for accurate position measurements. The sharpness of dots in the filter output image is dependent on the size of the convolution filter. For example, an 8 x 8 filter produces a sharper image of dots than a 4 x 4 filter. However, as the filter size increases, so does the million-instructions-per-second (MIPS) requirement of the image processing system.

Key accomplishments:

• Developed a spatial convolution filter mask for applications requiring precise position measurement using a digital camera system. This technique may be used in applications requiring a high-accuracy measurement of 3-D spatial coordinates where direct physical measurement is not practical.
• The block convolution filter designed for this application converts a printed target of alternating squares (checkerboard) to a set of pinpoints, thus minimizing dimensional error in the object being imaged.

Figure 2. Example 4 x 4 BCM

Figure 3. Input: BCM and Target Image

Figure 4. Output: Filtered Target Image Using BCM

Figure 5. Precision Position Measurement Application Using a BCM and 2-D Image Filter

Contact: Dr. R.C. Youngquist (Robert.Youngquist-1@ksc.nasa.gov), YA-C3-E, (321) 867-1829
Participating Organization: Dynacs Inc. (Dr. J.E. Lane and Dr. C.D. Immer)