We consider the problem of detecting jump location curves of regression surfaces when they are spatially blurred and contaminated pointwise by random noise. This problem is common in various applications, including equi-temperature surface estimation in meteorology and oceanography and edge detection in image processing. In the literature, most existing jump-detection methods are developed under the assumption that there is no blurring involved, or that the blurring mechanism described by a point spread function (psf) is completely specified. In this article, we propose four possible jump detectors, without imposing restrictive assumptions on either the psf or the true regression surface. Their theoretical and numerical properties are studied and compared. We also propose a new quantitative metric for measuring the performance of a jump detector. A data-driven bandwidth selection procedure via the bootstrap is suggested as well. This article has supplementary material online.