an example ... say.. a finger print image, which has ridges... i am talking about that broken ridges...( curved).. i think.. morphological operation.. with closing may work...
may be chosing of appropriate.. structuring element... will be challenging...
Morphological operations such as closing, using linear structuring elements of various orientations may be a method of choice. You can find details in the following publication:
Terol-Villalobos, I. R.; Morales-Hernández, L. A. & Herrera-Ruiz, G. Directional Structures Detection Based on Morphological Line-Segment and Orientation Functions Discrete Geometry for Computer Imagery, Springer Berlin / Heidelberg, 2008, 4992, 458-469
Otherwise, Gabor filters may also be of interest.
Article Directional morphological filtering
Conference Paper Directional Structures Detection Based on Morphological Line...
Do you have a model or some knowledge of the image capturing process that can differentiate between 1) a "real" broken line and 2) an apparent broken line that, in reality, is not broken? What about comparing the images with the actual objects?
I think you need such truths and such models so you can optimize your image processing algorithm(s).
@Leio. To what to you attribute the brokenness to? Is it instrumentation noise? Is it due to locally low contrast? Is it due to a variegated background or a variegated object? Is it due to low spatial or intensity resolution? What is your theory?