Correction of Inhomogeneous Illumination

Every real-world application has to contend with uneven illumination of the observed scene. Even if we spend a lot of eff ort optimizing the illu- mination setup, it is still very hard to obtain a perfectly even object irra- diance. A nasty problem is caused by small dust particles in the optical path, especially on the glass window close to the CCDsensor. Because of the distance of the window from the imager, these particles — if they are not too large — are blurred to such an extent that they are not directly visible. But they still absorb some light and thus cause a drop in the illumination level in a small area. These eff ects are not easily visible in a scene with high contrast and many details, but become very apparent in the case of a uniform background (Fig. 10.4a and b). CCD sensors also show an uneven sensitivity of the individual photoreceptors which adds to the nonuniformity of the image. These distortions severely limit the quality of the images. These eff ects make it more diffi cult to sepa- rate an object from the background, and introduce systematic errors for subsequent image processing steps.

Nevertheless, it is possible to correct these eff ects if we know the nature of the distortion and can take suitable reference images. In the following, we study two cases. In the fi rst, we assume that the gray value in the image is a product of the inhomogeneous irradiance and the refl ec- tivity or transmissivity of the object. Furthermore, we assume that we can take a reference image without absorbing objects or with an object of constant refl ectivity. A reference image can also be computed, when

258                                                                                               10 Pixel Processing

 

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Figure 10.10: Correction of uneven illumination with an inhomogeneous point operation: a original image and b its histogram; c background image and d its histogram; e division of the image by the background image and f its histogram.

 

small objects are randomly distributed in the image. Then, it is suffi - cient to compute the average image from many images with the objects. The inhomogeneous illumination can then be corrected by dividing the image by the reference image:

G ' = c · G / R.                                              (10.18)

10.3 Inhomogeneous Point Operations†                                                        259

 

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Figure 10.11: Contrast-enhanced a dark image and b reference image for a two-point radiometric calibration of a CCD camera with analog video output.

 

The constant c is required to represent the normalized image with inte- ger numbers again. If the objects absorb light, the constant c is normally chosen to be close to the maximum integer value. Figure 10.10e demon- strates that an eff ective suppression of inhomogeneous illumination is possible using this simple method.

 

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