Method for cleansing by removing unwanted data of inadvertently captured surfaces of optically captured, virtual representations of teeth and intraoral structures, wherein the method comprises the following steps: a. defining an extension line of the representation by the steps of: a.i. determining features which are prominent characteristics in a topography of the surface of the representation in the representation, a.ii. generating a two-dimensional point cloud by projecting points at which the features are located onto an extension projection plane, a.iii.forming a graph, specifically a curve, which extends along the point cloud generated in a.ii., a.iv. defining the curve generated in a.iii as the extension line, b. generating a projection plane at a point of the extension line, the extension line being normal to the generated projection plane at this point, c. projecting all known spatial points of the representation from one region on the projection plane onto the projection plane, wherein the corresponding spatial point is stored for each projected point, d. generating a two-dimensional curve on the projection plane from the projected points, e. determining maxima, minima and a center of the curve generated in step d., f. identifying projected points on the curve generated in step d. that are outside the outer minima or maxima when viewed from the center of the curve generated in step d., g. removing the spatial points that correspond to the projected points that were identified in step f., h. repeating the process from step b. if necessary for another point on the extension line. a. defining an extension line of the representation by the steps of: a.i. determining features which are prominent characteristics in a topography of the surface of the representation in the representation, a.ii. generating a two-dimensional point cloud by projecting points at which the features are located onto an extension projection plane, a.iii.forming a graph, specifically a curve, which extends along the point cloud generated in a.ii., a.iv. defining the curve generated in a.iii as the extension line, a.i. determining features which are prominent characteristics in a topography of the surface of the representation in the representation, a.ii. generating a two-dimensional point cloud by projecting points at which the features are located onto an extension projection plane, a.iii.forming a graph, specifically a curve, which extends along the point cloud generated in a.ii., a.iv. defining the curve generated in a.iii as the extension line, b. generating a projection plane at a point of the extension line, the extension line being normal to the generated projection plane at this point, c. projecting all known spatial points of the representation from one region on the projection plane onto the projection plane, wherein the corresponding spatial point is stored for each projected point, d. generating a two-dimensional curve on the projection plane from the projected points, e. determining maxima, minima and a center of the curve generated in step d., f. identifying projected points on the curve generated in step d. that are outside the outer minima or maxima when viewed from the center of the curve generated in step d., g. removing the spatial points that correspond to the projected points that were identified in step f., h. repeating the process from step b. if necessary for another point on the extension line.