This paper presents an application of marker-controlled segmentation in petroleum engineering. The images to be segmented originate from high resolution conductivity measurements of borehole walls. These measurements reflect the composition and structure of the rock formation through which the well was drilled. In this application, we detect and measure small cavities in the walls. These cavities are called vugs. We use the tools provided by mathematical morphology. Our strategy is based on gradient image modification using markers and on the watershed transformation. First, the vugs are automatically marked, as well as the background. These markers together delineate areas of interest in which we know there is one contour per vug. In order to find the vug contour and perform measurements, we modify the gradient image in such a way that only a single edge is kept between the vug and the background markers. We perform the final step of edge detection using the watershed transformation of the modified gradient image. The final result is one closed contour per marked vug. We present this strategy in detail, show experimental results and discuss artifact elimination.