8/2/2019 An Intuitive Explanation of Medial Axis Transformation

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AN INTUITIVE EXPLANATION OF MEDIAL AXIS TRANSFORMATION

Images A-D show some ideas of Harry Blum, inventor of the medial axis transform. Whereas ripples on water traverse through eachother (A), one also find 'waves' that can blockeach other (B). As example, Blum imagined fires starting at two points in a field ofgrass. They spread and eventually meet along a line (the medial axis) exactly equidistant between the two starting points (B). Theystop because no grass is left behind where either of the fires already swept by. A fire, started along a triangular outline (C), stopsalong the 'Y'-shaped medial axis inside the figure. Blum showed that grass fires are equivalent to tracing the centres of the largest(maximal) discs that can just fit into the outline figure (D). (E) shows the medial axis transform (MAT) of a human figure.

Our HST model uses Blum's concept, but has a shunting mechanism to let computational 'grass fires' burn only a fraction of the 'grass'they spread through in the 'field' of image pixels. Fires that burn very small fractions of grass (weak shunting), resemble ripples onwater (F). When fires burn all the grass (strong shunting), they behave as blocking wave fronts (G). We call this tunable method ofmedial axis transformation the Hybrid Symmetry Transform, or HST.

HST is elegant for several reasons. It is based on a silicon shunting inhibition network, proposed by Carver Mead (Analog VLSI andNeural Systems,1989). It further deals with noise in a particular way. Consider the MAT or HST for a trilobed amoeba shape (H). Withnoise dots added, the MAT is highly scattered (I) and resembles the medial axes between the closest data points (similar to HST withstrong shunting). But with HST shunting set between weak and strong values, the original medial axis transform of the amoeba shapereappears (J).

Why would a study of human visual perception be concerned with medial axis transformation? I. Kovacs et al. (Vis. Res., 38(15/16),1998) have shown that human visual sensitivity changes drastically depending on where they look within an outline figure (the whiteline figure in K is known as a cardioid shape, and its HST is shown in black). The HST output in both vertical and horizontal crosssections (L) closely matches Kovac's computational results. It also closely matches human perceptual sensitivity changes (M)measured for that particular outline figure. With these specific parameters values, the HST predicts human perceptual sensitivity mapsfor other figures. We applied the HST to reveal some of the implicit visual structure in Ryoanji (100k PDF. Van Tonder, Lyons & Ejima,

Nature, 419:359-360. 2002, and 60k PDF supplementary material), a well known Japanese Zen garden. T.S. Lee et al. (Vis.Res.,38(15/16), 1998) found evidence that neurons in the primate visual system respond to medial axes. In a collaboration with Dr. S. Oka,we used EEG analysis to show that symmetry axes play a role in human shape detection (342K PDF. Oka, Van Tonder & Ejima,

Vision Research, 41:3791-3803, 2001).

AN INTUITIVE EXPLANATION OF MEDIAL AXIS TRANSFORMATION 11-03-2012

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8/2/2019 An Intuitive Explanation of Medial Axis Transformation

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Extracting the darkest 'ridges' from the medial axis transform gives the medial axes of that figure (N). Medial axes are used ascompact descriptions of more complex shapes in engineering applications involving pattern recognition. Links to many other industrialuses for medial axis transformation can be found HERE.

Read more about the HST model developed in this research 293K PDF. Van Tonder & Ejima, IEEE SMC B, 33(3):535-541, 2003, .

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AN INTUITIVE EXPLANATION OF MEDIAL AXIS TRANSFORMATION 11-03-2012

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http://www.cis.kit.ac.jp/~gert/index.htmlhttp://www.cis.kit.ac.jp/~gert/g/res/web/publications/2003_IEEESMC_GVT_YE.pdfhttp://www.ics.uci.edu/~eppstein/gina/medial.html