General linear and nonlinear smoothing in an intensity image can blur corners seriously, so it's difficult to detect corners by a multi scale approach. But nonlinear multi scale CB (contour-based) morphological filters have a wonderful feature of keeping corners, at the same time it ensures that corners have the feature of monotonicity, which means non creation of new corners when the scale turns larger. Filtering the intensity image by CB morphological filters, the idea of CB morphological scale space is constructed, by which to realize multi-scale corner detection. Theory analysis and experimental results demonstrate the effectiveness of the new way.