In the last stage of colored point cloud registration, depth measurement errors hinder the achievement of accurate and visually plausible alignments. Recently, an algorithm has been proposed to extend the Iterative Closest Point (ICP) algorithm to refine the measured depth values instead of the pose between point clouds. However, the algorithm suffers from numerical instability, so a postprocessing step is needed to restrict erroneous output depth values. In this paper, we present a new algorithm with improved numerical stability. Unlike the previous algorithm heavily relying on point-to-plane distances, our algorithm constructs a cost function based on an adaptive combination of two different projected distances to prevent numerical instability. We address the problem of registering a source point cloud to the union of the source and reference point clouds. This extension allows all source points to be processed in a unified filtering framework, irrespective of the existence of their corresponding points in the reference point cloud. The extension also improves the numerical stability of using the point-to-plane distances. The experiments show that the proposed algorithm improves the registration accuracy and provides high-quality alignments of colored point clouds.