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1 Missing pixel correction algorithm for image sensors B. Dierickx, Guy Meynants IMEC Kapeldreef 75 B-3001 Leuven tel fax Paper or poster submitted for Europto-SPIE / AFPAEC May Zurich, CH Version 9-Apr-98 Printed on 05/15/98 3:49 PM

2 Missing pixel correction algorithm for image sensors Bart Dierickx and Guy Meynants IMEC, Kapeldreef 75, B-3001 Leuven, Belgium ABSTRACT We describe a compact algorithm that can on the fly detect and correct isolated missing pixels in the output stream of an image sensor, without significantly degrading the image quality. The algorithm is in essence a small kernel non-linear filter. It is based on the prediction of the allowed range of gray values for a pixel, from the gray values of the neighborhood of that pixel. A few examples will illustrate the effect of the algorithm on realistic images. 1. IMAGE SENSOR PIXEL DEFECTS AND IMAGE QUALITY One of the most important specifications of an image sensor is the "cosmetic quality": a sensor s image should be flawless. Unfortunately, the technology is not perfect. Due to processing imperfections, statistics, etc., a finite number of pixels in a sensor array will be defective (hard faults) or yield a signal that deviates visibly from the "exact" pixel gray value (soft faults). Such faults appear as white or black (or gray) points in the image. For a human observer, these tend to be much more annoying than other image imperfections as temporal noise, a mild fixed pattern, or imperfect registration of color or gray values. A way to cancel these spots is to store a list of these and of their positions in the image in a memory. In an image processing step the faulty pixel gray value is then replaced by e.g. the average of the surrounding pixels. This method is viable, but has the disadvantage that it requires a memory. Moreover, it cannot handle pixels faults that appear intermittently or only in certain cases. A good example is a so-called dark current pixel. Such pixels will appear white in a dark environment, but will behave normal in a bright environment. Other ways to cancel isolated pixels faults are spatial median filters and variants thereof. Unfortunately such filters do also remove useful detail from the image. As an example, consider the image of a star covered sky with an image sensor that has some faulty pixels that appear white. The quoted filters are not able to remove the white point due to faults, and leave the white points that are stars untouched. Fig. 1. (a) Left: image of a point light source on a dark background (b) Right: defect white pixel 2. A MISSING PIXEL REPLACING ALGORITHM An image projected through a lens or any other optical device is never perfectly sharp. Even with ideal lenses, a star image is not projected on a single pixel. The point-like source of the star will be smeared out over a central pixel and a few neighbors (Fig. 1). In a one-dimensional cross section through the image, a star will look like fig. 2 (a), while a white pixel fault might look like fig. 2 (b). In the simple example of figures 1 and 2, the peak in (b) should be removed, while the peak in (a) should remain. dierickx@imec.be, meynants@imec.be WWW:

3 The goal is clear: only device faults are corrected, while normal images are left untouched. The operation should cause no visible image degradation in faultless parts of the image. For fig. 1.a. and fig. 2.a., it is clear from the neighborhood that there should be a peak. The gray level gradients in the neighborhood suggest and upper (and a lower) limit for the central pixel; the peak s gray value should be between these limits in order to match the expectations from the neighborhood.. We try to express this in a concise algorithm or non-linear spatial filter as a method to remove an isolated whiter or darker pixel from an image. We limit the value of every individual pixel between an upper and a lower bound that are derived from the values of pixels in the immediate neighborhood of the scrutinized, central, pixel. These upper and lower bounds are found by extrapolation of the neighborhood pixel gray values towards the position of the central pixel. intensity white black cmax cmin (a) (b) a b c d e x-axis a b c d e x-axis Fig. 2. (a) image of a point source (b) white spot due to pixel defect In a formula We use in this example a 5 1 kernel (a,b,c,d,e). The most straightforward set of limiting values is the linear extrapolation from two times two neighbors left ( a, b ) and right ( d, e ) of the central pixel c. The upper bound of c is calculated as cmax = MAX(2b-a,2d-e,b,d) (1a) together with the lower bound cmin = MIN(2b-a,2d-e,b,d) (1b) The corrected c-value is then be obtained as c = MEDIAN(c,cmin,cmax) (1c) The extrapolated value is thus calculated as 2*b-a, or more general: b + n * (b-a) (1d) where n is a real number. In this case, a 5 pixel kernel is used. We have the experience that smaller kernels do not yield good results. Larger and twodimensional kernels may give improvements compared to the 5-pixel kernel. Yet the one-dimension kernel described here has the advantage that it can be processed on a sequential stream of pixel data, without the need of a line memory or image memory. It can also correct vertical line flaws, the most common type of extended fault in an image sensor. 3. EXAMPLES Figure 3 is an image taken with the Fuga15d [1] camera. The camera typically has a few white pixels, but for demonstration purposes, a large number of white defects has been added in firmware, as was the white pixel correcting filter. Figure 4 is taken with the unmodified camera; here the detail contains a real white pixel defect. Both examples demonstrate that the algorithm can correct isolated defects (and also vertical line defects) to a nearly invisible level. Isolated pixels in an otherwise

4 homogeneous background disappear perfectly. Also the speckles due to temporal noise or fixed pattern noise are somewhat suppressed (fig. 4). The algorithm has the tendency to smoothen sharp lines and points. The distinction between a projected point and a pixel defect depends on the sharpness or MTF of the optical system. A sharper optics requires a higher n in formula (1d), and should be tuned according to the camera MTF performance. Fig. 3. a) Upper left: 256x256 cut-out of original image, with random white pixels artificially added. b) Upper right: image processed through the present algorithm c) Lower left: image (a) off-line 2 x 2 median-filtered. Defects on intensity gradients or on edges are corrected imperfectly by the simple algorithm. Although the situation where this is visible is rare, we can solve this by adding intensity gradient correction to the algorithm. A simple variant of the algorithm (1) which behaves better near edges, is: cmax = MAX(AVERAGE(b,d), 2b-a,2d-e) (2a)

5 cmin = MIN(AVERAGE(b,d), 2b-a,2d-e) c = MEDIAN(c,cmin,cmax) (2b) (2c) a. b. c. Figure 4. Detail of an image with a white pixel defect. (a) from the original image, (b) after applying the present algorithm, (c) 2x2 median filtered image mosaic color filter image sensors A difficulty arises when one tries to use the algorithm on the image of a mosaic color filter image sensor. The algorithm cannot distinguish between defect pixels and pixel with a deviation response due to the color of the scene. The algorithm is applicable though on the reconstructed RGB (or YUV) signals, on the condition that they are reconstructed in a way that an isolated pixel defect results in isolated faulty pixels in each of the R, G and B channels. software and hardware implementations Implementations of the above algorithms in software and firmware, analog hardware or digital hardware are possible. A specific stream or pipeline implementation is straightforward to realize as the kernel is small and requires no memory. An analog domain implementation of the above algorithm, for application on a video stream has been realized [2]. REFERENCES [1] B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, J. Vlummens, "Random addressable active pixel image sensors", at AFPAEC Europto/SPIE, Berlin, 9 Oct Published in SPIE proceedings vol p.1. [2] G. Meynants, B. Dierickx, A circuit for the correction of pixel defects in image sensors, submitted ESSCIRC 1998

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