A system for generating an image of an elongate medical device, the system comprising: the elongate medical device defining a topological plane including a plurality of position sensors; a computer-based model construction system configured to be coupled to the elongate medical device and configured to acquire a set of measured data points corresponding to respective positions of the plurality of position sensors, the computer-based model construction system further configured to: establish a coordinate system associated with the elongate medical device; calculate a respective coordinate in the coordinate system for each of the plurality of position sensors; estimate a set of true parameters describing deviations from a parametric form of the elongate medical device, the set of true parameters including a constant curvature term and a constant torsion term defined by the surface of the medical device; calculate a measurement error (ε) for each of the plurality of position sensors based at least in part on a respective stiffness parameter, which is a parameter that defines how much variation in the measured data point of each sensor is permitted; compute smoothed data points for the plurality of position sensors based on the sum of (i) a function of the estimated set of the true parameters and the respective coordinates of each of the plurality of position sensors, and (ii) a smoothed fraction of the measurement error (ε); generate an image of the elongate medical device using the smoothed data points; and display the generated image. the elongate medical device defining a topological plane including a plurality of position sensors; a computer-based model construction system configured to be coupled to the elongate medical device and configured to acquire a set of measured data points corresponding to respective positions of the plurality of position sensors, the computer-based model construction system further configured to: establish a coordinate system associated with the elongate medical device; calculate a respective coordinate in the coordinate system for each of the plurality of position sensors; estimate a set of true parameters describing deviations from a parametric form of the elongate medical device, the set of true parameters including a constant curvature term and a constant torsion term defined by the surface of the medical device; calculate a measurement error (ε) for each of the plurality of position sensors based at least in part on a respective stiffness parameter, which is a parameter that defines how much variation in the measured data point of each sensor is permitted; compute smoothed data points for the plurality of position sensors based on the sum of (i) a function of the estimated set of the true parameters and the respective coordinates of each of the plurality of position sensors, and (ii) a smoothed fraction of the measurement error (ε); generate an image of the elongate medical device using the smoothed data points; and display the generated image. establish a coordinate system associated with the elongate medical device; calculate a respective coordinate in the coordinate system for each of the plurality of position sensors; estimate a set of true parameters describing deviations from a parametric form of the elongate medical device, the set of true parameters including a constant curvature term and a constant torsion term defined by the surface of the medical device; calculate a measurement error (ε) for each of the plurality of position sensors based at least in part on a respective stiffness parameter, which is a parameter that defines how much variation in the measured data point of each sensor is permitted; compute smoothed data points for the plurality of position sensors based on the sum of (i) a function of the estimated set of the true parameters and the respective coordinates of each of the plurality of position sensors, and (ii) a smoothed fraction of the measurement error (ε); generate an image of the elongate medical device using the smoothed data points; and display the generated image.