Course on

Advanced Morphological Signal/Image Processing


Seminar in the framework of the "Master en Technologías, Sistemas y Redes de Comunicación "

Escuela Técnica Superior de Ingenieros de Telecomunicación - Universitat Politècnica de València - April 2010



Duration: 10 hours


Lecturer: Jesus Angulo, Centre de Morphologie Mathématique, MINES ParisTech, France


Prerequisites: A basic course on morphological image processing


Material: Slides in English, with detailed technical description of operators and filters, illustrated with signal and image examples, and references to main publications


Evaluation: Two exercises to be solved after the course (homework)




Part I. Elements of morphological filtering [Slides]


1. Remind on fundamental morphological operators

2. Gradients and top-hats

3. Granulometry and pattern spectrum

4. Alternate filters and other products of openings and closings

5. Contrast and center


Part II. Self-dual morphological operators and filters [Slides]


1. Self-duality in signal/image processing

2. Median filter and robust modifications of median

3. Complete semilattice and operators

4. Erosion and opening in difference and reference semilattices

5. Leveling operator


Part III. Non-flat numerical mathematical morphology [Slides]


1. Volumic grey-level morphological operators

2. a-transformed grey-level dilation and erosion

3. Paraboloid structuring functions: “eigenfunctions” of the slope transform





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