Non-linear fourth-order image interpolation for subpixel edge detection and localization

A fourth-order non-linear interpolation procedure based on the ENO (Essentially Non-Oscillatory) methodology is presented and evaluated, with the purpose of increasing the geometric accuracy of edge detection in digital images. Two possible cases are considered one that considers that each pixel of the image represents a point value, the other that the pixel is an average value of a function. After image interpolation to obtain a finer grid of pixels, the Canny edge detection algorithm is applied, with the objective of improving the localization and geometry of the edges at a subpixel level. The results are compared with other schemes based on fourth order two-dimensional interpolation methods, such as a centered scheme based on a cubic convolution, a fourth order non-centered lineal scheme and a centered cubic convolution based on local gradient features. The evaluation is performed using visual and analytical techniques applied over aerial and satellite images, analyzing the positional errors of the detected edges, as well as the errors due to changes in scale and orientation. In addition to the subpixel edge detection, the quality of the interpolated images is tested. We conclude that the proposed methodology based on ENO interpolation improves the detection of edges in images as compared to other fourth-order methods.