Camera calibration using planar targets has been widely favored, and two types of control points have been mainly considered as measurements: the corners of the checkerboard and the centroid of circles. Since a centroid is derived from numerous pixels, the circular pattern provides more precise measurements than the checkerboard. However, the existing projection model of circle centroids is biased under lens distortion, resulting in low performance. To surmount this limitation, we propose an unbiased projection model of the circular pattern and demonstrate its superior accuracy compared to the checkerboard. Complementing this, we introduce uncertainty into circular patterns to enhance calibration robustness and completeness. Defining centroid uncertainty improves the performance of calibration components, including pattern detection, optimization, and evaluation metrics. We also provide guidelines for performing good camera calibration based on the evaluation metric. The core concept of this approach is to model the boundary points of a two-dimensional shape as a Markov random field, considering its connectivity. The shape distribution is propagated to the centroid uncertainty through an appropriate shape representation based on the Green theorem. Consequently, the resulting framework achieves marked gains in calibration accuracy and robustness. The complete source code and demonstration video are available at https://github.com/chaehyeonsong/discocal.