A new local edge detection method is proposed that is effective on multivariate irregular data in any domain. The method is numerically cost efficient and entirely independent of any specific shape or complexity of boundaries. Application of the minmod algorithm to various orders of the method ensures a high rate of convergence away from the discontinuities while reducing the inherent oscillations near the discontinuities. It further enables distinction of jump discontinuities from steep gradients, even in instances where only sparse non-uniform data is available. The method is successfully demonstrated in both one and two dimensions. This method is compared to previously designed edge detection methods based on spectral data. It is well known that edge detection is critical for the reconstruction of an image where the underlying function is piecewise smooth. Many images are obtained from equally spaced data points. In this case, our method can determine regions of smoothness for the underlying function. Application of a high resolution reconstruction method, for example, the Gegenbauer reconstruction method, will then produce a highly resolved reconstruction of the desired image. Several examples are discussed.