Roof edge detection using regularized cubic b-spline fitting

1 Summary The extraction of roof edges requires the reconstruction of the original signal from a lattice of sampled values of grey level (i.e. the sampled image). This is an ill-posed task and therefore, adequate constraints of regularization have to be incorporated. A scheme employing one-dimensional Regularized Cubic B-Spline (RCBS) tting has been used successfully on the task of step edge detection, in which the regularized tting is transformed into a quadratic energy equation to simplify the computation. However, this scheme has three major limitations: it is non-linear; it has a limited accuracy; and it is computationally expensive. This paper presents a modiied scheme which overcomes these limitations. The modiied scheme employs the 1-D RCBS tting on the horizontal and the vertical orientations of a window of an image to generate two 1-D signals, which provide suucient information about the local property of the sub-image for roof edge detection. This paper also shows that the regularization factor should be suuciently large to make the computation well-conditioned. The modiied RCBS tting is used in a roof edge detector. Two parameters, the regularization factor and a threshold, are to be given a priori. Since determines the degree of smoothing, a larger value of should be used when the signal is noisy. Conversely, if the signal is noise-free, a small value of should be used so as to preserve the signal. The threshold reeects the size of an edge, i.e. the larger the edges to be detected, the larger the threshold. The False-Correct Ratio is used to quantitatively evaluate the performance of the roof edge detector on synthetic images. The roof edge map of a real image with step and roof edges shows that the proposed roof edge detector is more sensitive to arbitrary signal than a step edge detector. Abstract-A scheme employing one-dimensional Regularized Cubic B-Spline (RCBS) tting 18] has been used successfully on the task of step edge detection. The regularized tting is transformed into a quadratic energy equation to simplify the computation. This scheme however has three major limitations: it is non-linear; it has a limited accuracy; and it is computationally expensive. This paper presents a modiied scheme which overcomes these limitations. The modiied scheme employs the 1-D RCBS tting on the horizontal and the vertical orientations of a window of an image to generate two 1-D signals, which provide suucient information about the local property of the sub-image for …