Multiscale Feature Identification in the Solar Atmosphere C. Alex Young, Dawn C. Myers, Peter T. Gallagher (L-3 Communications GIS) SIRW at the ROB - Oct. 23-24, 2003

General Outline Motivation An Aside An event and a standard approach A Multiscale approach Some natural extensions - Beamlets, Ridgelets, Curvelets, and all that - Morphological Component Analysis.

Motivation To model a subjective feature detection method (an observer with a computer mouse, i.e. the point-and-click detector) with an objective detection method using a multiscale vision model. Try to track edges over multiple scales or resolutions using a wavelet based multiscale edge detector. This will then give us consistent, reproducible, and statistical features.

The Solar Physics Community has only scratched the surface. Tracking features with a mouse and a pen is only a start not science. We need to develop an image processing tree in solarsoft. Morphological transforms and wavelets are not cutting edge, they are simply a starting point and part of a basic toolset.

General Multiscale Transforms Neural Networks Support Vector Machines Markov Chain Monte Carlo Imaging Texture Modeling Multiscale Likelihood / Posterior Methods Non-linear filtering Maximum Entropy Information Theory Approach (Shannon Information)

The Event - April 21, 2002

Images at the time of the first brightening in the TRACE movie Images at the time of the first brightening in the TRACE movie. (Gallagher 2003) Top panels: TRACE 195 Å difference images created by subtracting each image from a frame taken at 00:42:30 UT. Bottom panels: LASCO C2 and C3 images showing the similar morphology of the eruption as it propagates away from the solar surface. (Gallagher 2003)

A Standard Analysis

Can we use a vision model to remove some of the subjectivity Can we use a vision model to remove some of the subjectivity? Say multiscale edges.

The Method A multiscale version of an edge detector is implemented by smoothing with dilated kernels θ. These kernels are B3 cubic splines which approximates a Gaussian. The detector is computed with two wavelets that are the first partial derivative of θ. The wavelet transform components are proportional to the gradient vector smoothed by θ. So the wavelet transform maxima at each scale size give us multiscale edges corresponding to curves of structure at a particular scale.

Wavelets and multiscale edges for 4 scales TRACE 195 Å image at 00:58:58 UT scale = 2 scale = 4 scale = 8 scale = 16

A set of edges from 00:46:34 UT to 01:01:58 UT at 2 scales The top image shows the 30 multiscale edges at scale 8 (green) and 16 (red) over the image at 00:46:34 UT. The bottom images zoom in on the fronts.

Following a front in TRACE.

The event in C2

At a fine and medium scale (no background model)

C2 edges for one scale size

Beamlets, Ridgelets, Curvelets and all that Wavelets are generally isotropic and best suited for representing point structures. If we extend the multiscale model from points to lines, curves and the like we can obtain a near optical representation. Combining different multiscale morphologies gives us Morphological Component Analysis

Beamlet (multiscale line-segments)

Ridgelet (wavelets in Radon space)

Curvelet (multiscale curves)

XMM image

Morphological Component Analysis à trous wavelet encoding ridgelet encoding

HST image of A370 ridgelet/curvelet encoding à trous wavelet encoding sum of all three

Conclusions The toolset for solar image processing needs to be made available to the community. (image processing branch in SSW - see Peter Gallagher) Wavelet based transforms provide a robust representation of many structures in solar images. The natural extension wavelet transforms is a general multiscale morphological method. Apply machine learning, probabilistic methodologies etc. to the represented structures.