My research work was instructed by Dr. Palaniappan and Dr. Tobias I. Baskin.Accurately estimate the growth rate of the plant root
This work explores the estimation of the growth rate of plant root by computing the velocity field from root image sequences. This project is directed by Dr. Tobias Baskin. The goal of my work is to get an accurate velocity profile over the elongating direction of the plant root.The measurement of the growth was done manually by Dr. Baskin's students to match local features of the plant root with bare eyes, which is not accurate and time consuming. We set the imaging interval between each consecutive root images to be 10 seconds, comparing with manual matching at an interval of half an hour.
Originally we used the images of the root of species Arabidopsis thaliana L., Latter we tried other root images. With the accurate growth profile over different parts of a plant root, biology scientists like Dr. Tobias Baskin can imagine, explain or predict the dividing behaviors of plant cells, the effects of hormones in growth and the effects of environment changes on the growth.
To develop an efficient algorithm to measure the growth of plant root was inspired by the success of the project in the Univ. of Heidelberg to estimate the growth of leaves. While in our experiment we found that the method used to measure the growth of leaves, which is called structure tensor-based motion estimation method, is not enough to accurately compute the velocity fields of plant root. One reason is that under the microscope, the plant may "grow" much faster than leaves, which make the assumption "low-level motion" of the tensor-based method not applicable some times. Another reason is that this method is very sensitive to noise, and because of the aperture problem, the real velocity may not be able to compute because the plant root has not much texture like a leaf. We address these problems by combining the tensor-based method with robust matching method: when the velocity field is not suffering aperture problem and the local structure is good enough, we trust the output of the tensor-based method; otherwise, we use that output as an initial parameter to determine the searching domain and do robust matching to get the accurate velocity.
Finally we developed a software package called RootflowRT to estimate the growth profile of plant root under an integrated framework. There are two extra successes in this experiment, one is under this framework, we can do segmentation at the same time of getting the dense optical flow. Another is that we developed a set of confidence test to remove outliers in the velocity fields.
Plant Root Images
Here are the sample plant root images. We imaged 10 images for each segment of the plant root Arabidopsis thaliana L. with the image size 640x480. The root was growing in a glass chip full of nourishing water, and the skin of the root was covered by a layer of water rim.
Robust Matching Optical Flow Estimation
Robust matching algorithm is just do minimization of a robust objective function over two matching windows in a certain searching domain. In stead of using min-squared error as the objective function, robust matching method use much sharper function to find the the minimum. Normally we choose the objective function as f(x)=x/(a+x*x). The key of this method is choose appropriate local window size and the size of the search domain. The size of the searching domain will determine the total running time, and the window size choosing is subtle because if it is too big, it will suffer the motion deformation, and if it is too small, it will not capture the local structure(this will lead to a topic like making the window size adaptive). In our program, we choose window size to be 15pixels x 15 pixels, and if we can not get good velocity result when suffer deformations, the window size is changed to be 7x7 and do the searching again.One disadvantage of matching method is that it need a sort of global search to get the minimum, because it has no idea about the velocity from local information. So when some method like tensor-based method can give it this idea, the matching may not need to be global search and the running time is much shorter.
Check This paper to get idea of robust matching methods on plant root images.Structure Tensor-based Method for optical flow computation
Readers can find necessary introduction of tensor-based method in estimating the velocity from spatial-temporal volume:The tensor method can be derived from global minimization of integration of local derivatives, or be derived by estimating the orientation of the image volume. This method, though beautiful in mathematics induction, suffers aperture problem and sometimes may not capture the deformation of the images. Currently researchers like Machael J. Black want to catch the abrupt changes in images, together with similarity estimation. I think one great advantage of this method is that it can give hints to decide whether the motion exists or not, and also indicate the recognizability of local structure. So when it combine with robust matching method, it can initialize the matching method with a not accurate but close parameter for the searching domain.
You can download the source code for pure tensor method and the SGI executable package of the combined method at Available Software.
The result for the two image stacks using pure tensor method can be found here in PPM image format.
The result by combining these two methods can be found here.
Rootqt.mv is a quick time movie file which illustrates the root growth and the area with rich local structure in the xyt image volume where the motion can be safely extracted which is indicated by tensor confidence(=Edge + Corner) with considerable value.
Participation in Land Cover Land Use Classification Project
In the Fall semester of 1999, I had participated in the landcover project by programming image/map interfaces between BTGA program and the Erdas Imagine environment.
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