Blur kernel estimation is a crucial step in the deblurring process for images. Estimation of the kernel, especially in the presence of noise, is easily perturbed, and the quality of the resulting deblurred images is hence degraded. Since every motion blur in a single exposure image can be represented by 2D parametric curves, we adopt a piecewise-linear model to approximate the curves for the reliable blur kernel estimation. The model is found to be an effective tradeoff between flexibility and robustness as it takes advantage of two extremes: (1) the generic model, represented by a discrete 2D function, which has a high degree of freedom (DOF) for the maximum flexibility but suffers from noise and (2) the linear model, which enhances robustness and simplicity but has limited expressiveness due to its low DOF. We evaluate several deblurring methods based on not only the generic model, but also the piecewise-linear model as an alternative. After analyzing the experiment results using real-world images with significant levels of noise and a benchmark data set, we conclude that the proposed model is not only robust with respect to noise, but also flexible in dealing with various types of blur.