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This paper focuses on the use of mobile sensors to estimate contours in a field. In particular, we focus on strategies to estimate the contour with minimum latency and maximum precision. We propose a novel algorithm, ACE (adaptive contour estimation), that (a) estimates and exploits information regarding the gradients in the field to move towards the contour and (b) uses a spread component to surround the contour in order to optimize latency. While it is possible for sensors to spread as they approach the contour, it is crucial to judiciously determine when and how much to spread. Spreading too early or too much may result in increasing the latency or affecting the precision. ACE dynamically makes this decision using local sensor measurements, history of measurements as well as collaboration between sensors while adapting to different types of deployment, distance from the contour and shapes of the contour. We demonstrate that ACE, in the absence of energy constraints precisely determines the contour with a lower latency than when only gradients are used for movement or when the sensors spread out right from the start of estimation. Additionally, we show that ACE significantly improves precision of contour estimation in the presence of energy constraints. We also demonstrate a proof of concept implementation on a mobile robot testbed.