This article presents a novel framework that can generate a high-fidelity isosurface model of X-ray computed tomography (CT) data. CT surfaces with subvoxel precision and smoothness can be simply modeled via isosurfacing, where a single CT value represents an isosurface. However, this inevitably results in geometric distortion of the CT data containing CT artifacts. An alternative is to treat this challenge as a segmentation problem. However, in general, segmentation techniques are not robust against noisy data and require heavy computation to handle the artifacts that occur in three-dimensional CT data. Furthermore, the surfaces generated from segmentation results may contain jagged, overly smooth, or distorted geometries. We present a novel local isosurfacing framework that can address these issues simultaneously. The proposed framework exploits two primary techniques: 1) Canny edge approach for obtaining surface candidate boundary points and evaluating their confidence and 2) screened Poisson optimization for fitting a surface to the boundary points in which the confidence term is incorporated. This combination facilitates local isosurfacing that can produce high-fidelity surface models. We also implement an intuitive user interface to alleviate the burden of selecting the appropriate confidence computing parameters. Our experimental results demonstrate the effectiveness of the proposed framework.