Color lens shade compensation achieved by linear regression of piece-wise bilinear spline functions

Touraj Tajbakhsh

Abstract: The pixel densities of current CMOS sensors increase and bring new challenges for image sensor designers. Todays sensor modules with miniature lenses often exhibit a considerable amount of color lens shading. This shading is spatial-variant and can be easily identified when capturing a flat textureless Lambertian surface and inspecting the light fall-off and hue change from the image center towards the borders. In this paper we discuss lens shade compensation using spatially dependent gains for each of the four color channel in the Bayer color filter array. We determine reference compensation functions in off-line calibration and efficiently parameterize each function with a bilinear spline which we fit to the reference function using constrained least-squares and Lagrangian conditions ensuring continuity between the piece-wise bilinear functions. For each spline function we optimize a rectilinear grid on which the spline knots are aligned by minimizing the square errors between reference and approximated compensation function. Our evaluations provide quantitative results with real image data using three recent CMOS sensor modules.