This study presents an experimental investigation on the local curvature of the bubble interface and its relation to local bubble growth regimes and bubble detachment. An experimental facility has been built in order to produce bubbles by nucleating on a 180-mu m-diameter artificial nucleation site on a horizontal copper surface. High-speed videography was used to observe and capture the boiling phenomenon, and an image-processing code has been developed in order to determine the local curvature of the bubble interface through the two main radii of curvature. As the evolution of the curvature at the apex of the bubble reflects the evolution of the vapor pressure inside the bubble, it is shown that inertia plays a negligible role and that bubble growth is dictated by thermal diffusion considerations. The measured curvature profile along the bubble has been compared to the hydrostatic Young-Laplace curvature relation. It is observed that the curvature profile near the base diverges from the theoretical prediction as the bubble forms a neck during its growth. This observation can be related both to the successive stages or regimes of growth and to the mechanism of bubble detachment.