Jasper van de Gronde

• room number: 491 (Bernoulliborg, building 5161)
• e-mail: j.j.van.de.gronde rug.nl

Research interests

I am interested in all sorts of image processing topics, including compressed sensing, linear and morphological filters, and deep learning, with a special interest in applications on large/high-dimensional and non-scalar data. Making proper use of vector- or tensor-valued data, possibly as an intermediate step, also interests me greatly, as does the interplay between (mostly) linear approaches and morphological approaches. My PhD thesis was on morphological operators for tensor images, exploring shape and structure in movement and direction dependence. I defended my thesis on 30 June 2015, and am currently a post-doc.

Tensor images (or volumes) are just like ordinary images or volumes, except that at each point we have a vector or matrix (tensors are essentially a generalization of vectors and matrices). To visualize a tensor image with matrices at each position, we typically use "glyphs": for each position a small glyph is drawn whose shape represents the matrix (S). The glyph is often a unit sphere deformed in such a way that each vector v on the unit sphere is given the magnitude v.(S.v). Below you can interact with a live demonstration of this technique (requires a WebGL capable browser, I recommend Firefox, and possibly some patience):

Demos

Apart from the rendering above, here is some more code you can try out both in the browser and using Node.js:

• Group-invariant frames for colour morphology. This tries to make "false" colours much less objectionable by using group invariant frames (and thereby operators).
• Frames for Tensor Field Morphology. Uses rotation-invariant frames to apply morphological filters to structure tensors.
• Path-based mathematical morphology on tensor fields. Path openings on general directed acyclic graphs derived from tensor fields.
• Efficient and Robust Path Openings using the Scale-Invariant Rank Operator. Generalized path openings on binary images and greyscale sequences.

There are also some demos that can only be run off-line:

• Group-invariant colour morphology based on frames. Similar to other previous demo concerning group-invariant frames, but also has code for performing a simple classification task. (Python)
• Frames, the Loewner order and eigendecomposition for morphological operators on tensor fields. Demonstration of various methods for computing morphological filters on tensor fields. (Python)
• Fast Computation of Greyscale Path Openings. Novel algorithm for computing greyscale path openings on images. (C++)
• Tensorial Orientation Scores. Computes tensorial orientation scores. (Mathematica)
• Generalized Morphology using Sponges. Simple example of filtering angle-valued signals. (Mathematica)

Various projects not (necessarily) associated with a particular publication can be found on Github (also see the SciJS repository).

Further information and links

I maintain a bibliography of work done on both colour morphology and tensor morphology (note that I'm not too strict about what classifies as "colour" morphology). I try to subclassify (using tags) papers based on what kind of method they use. If you feel anything is missing or wrong, please let me know.

An interesting (informal) discussion of the problem of finding a total order for colours can be found here. Note that most of the approaches discussed there indeed correspond to actual algorithms that have been tried in mathematical morphology (and the overview is even fairly, although not entirely, complete). In particular, people have experimented with methods similar to the Hilbert curve approach (Chanussot1998), as well as the travelling salesman approach (Florez2005, Chevallier2014). But note that Chevallier has shown that any total order is necessarily discontinuous when computing joins and meets (this is part of the reason why much of my thesis is focussed on making partial orders more palatable).

Although I tend to talk about product orders and lexicographical orders, there are many more related concepts, as well as different terms for the same concepts. To clarify, I have made a short summary of different terms and in which context they are used.

Publications

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