Tracking Turbulent 3D Features

Lu Zhang

Nov. 10, 2005

Motivations

Introduction Visualization techniques can help scientists to identify observed

phenomena both in scientific simulation or practical circumstance.

Application Storm, Hurricane, Ocean wave, Cloud….

Common features:• multiple evolution • time-varying• huge dataset• non-rigid

Outline

Segmentations and Region growing Thresholding Region growing

Features extraction Different features

Classification and Feature tracking Tracking methods Classes and structures

Overview

The original dataset

Flowchart and Modulus

Input imagesSegmentation

Feature extraction

Classification

Graph building

Basic features

classes

Directed acyclic graph

Segmentations and Region growing Thresholding Global thresholding vs optimal thresholding

Region Growing method Iterative region growing method [1]

Segmentations and Region growing Region Growing Basic features

timeID viewID x y R G B

Features extraction

Feature structure

After gaining region information from segmentation stage, we can browse each region to find basic features Areas – The count of all pixels in the region. Center of Gravity –The center of all points in one region. Diameter - Diameter is the distance between two points on the

boundary of the region whose mutual distance is the maximum. Perimeter - The number of pixels under each edge label. Fourier descriptors – Fourier transform of boundary points.

Features extraction

Output from Feature extraction module viewID mx my areas labeling timeID …..

Classification /Feature tracking

ClassificationAfter feature extraction module, we can gain a list of feature information for each region in different views.

One AssumptionBecause all the views have strictly time order, we can assume the difference between a pair of views should not vary too much.

Classification /Feature tracking

Evolution in time-varying imagesThere are five different changes of regions between a pair of views.

Continuation: one feature continues from dataset at t1 to the next dataset at t2

Creation: new feature appear in t2 Dissipation: one feature weakens and becomes part of the background Bifurcation: one feature in t1 separates into two or more features in t2. Amalgamation: two or more features merge from one time step to the

next.

Classification /Feature tracking

Classification Several pattern recognition methods can be used here,

eg. Euclidean Distance classifier:

KNN classifier: Find the K-Nearest Neighbor feature clusters in datas

et t1 and dataset t2.

Aeuc xAxd ,

Classification /Feature tracking

Output from Classification module

I create a new class to preserve the output dataset from Classification module: class LabelTrack(). It preserve the information:

1. ViewID: camera positions, we will move camera around the object in order to restore 3D object.

2. timeID: time order, for each camera position , we will take several time- varying images

3. classID: class number after correspondence computation between a pair of images in time order

4. Label: the original region numbers before correspondence computaton

5. R, G, B: the color information for each pixel

6. Coordinate x, y: the 2D coordinate of the projection of 3D object.

7. Forward pointer: preserve the labeling information of the previous dataset

8. Backward pointer: preserve the labeling information of the next dataset

Computation Time

The importance of computation time Size of database:

512*512*24*40(time orders)*N(camera positions)

In [5], the resolution is 128^3 with the computation time: 40 minutes.

In my project, I use 3 minutes for 512*512*24*40. Because this is the framework of the whole project, there are a lot of I/O operations to see the temporary results. My expectation is 1 minutes for each camera position finally.

REFERENCES

[1] Snyder and Cowart, “An Iterative Approach to Region Growing”, IEEE transaction on PAMI, 1983

[2] Wesley E.Snyder and Hairong Qi, “Machine Vision”, Cambridge [3] Richard O.Duda, Peter Hart, David Stork, “Pattern Classification”, Prenti

ce Hall [4] Rafael Gonzalez, Richard Woods,”Digital Image Processing”, 2nd, Prenti

ce Hall [5] D.Silver, Xin Wang, ”volume tracking”, Visualization '96. Proceedings.27

Oct.-1 Nov. 1996

Thanks

Any questions?