Center for Bio-Image Informatics

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Elisa Drelie Gelasca, ^1,2Emre Sargin,^1,2 Ken Rose^1,2, B. S. Manjunath^1,2

¹Department of Electrical and Computer Engineering, ²Center for Bio-image Informatics, University of California, Santa Barbara, CA.

Abstract

Tracing of curvilinear structures is one of the fundamental tools in the quantitative analysis of biological images, for extracting information about structures such as blood vessels and microtubules, and similar entities. Microtubules are tubulin polymer structures in cell bodies which are crucial in the mitosis, intra-cell transportation, and are a component of the cell's cytoskeleton. Researchers believe microtubules play a important role in Alzheimer's and in certain cancers. Presently, biologists are studying how these structures grow and shorten in the presence of certain key proteins such as Tau and with various drugs in the hope of understanding how they contribute to these diseases. The measurements of these microtubules with current techniques are very labor intensive. Therefore, automatic algorithms which will ideally trace microtubules with minimal human input are suited. Due to the limitations in biological sample preparation and fluorescence imaging, typical images in live cell studies exhibit severe noise and considerable clutter and automatic microtubule tracing becomes an hard task An automatic method has been proposed in in [1] for extracting curvilinear structures from live cell fluorescence images, but before biologists adopt new automated tracing algorithms, the performance has to be proven. We propose an evaluation method to compare the tracing results to ground truth data. The groun truth manually obtained from different experts is available for downloading.

Dataset and Ground Truth

Tracing results and ground truth from 4 different experts can be downloaded here. In evaluating, we adopted [1] method to trace MTs in live cell images obtained from Stuart Feinsten's Lab. The ability of tracking individually
selected MTs is ultimately important for biological research.

Click on each thumbnail to see the tracing evolution in the original video, leading to the segmentation of a stack of microtubule (mt_tracing_output.mat) that can be downloaded along with the manual segmentation of 4 different experts (gt_expert#). The key idea of the tracing algorithm is to propagate the trace from an initial point on the curve in all directions and select the best trace whose convolution with a kernel, representing the distortion, approximates the observation. For a given starting point on the structure, all possible paths can be represented by a graph (tree) with a branching factor of 8, where the vertices correspond to image pixels and the edges correspond to the directional weights. Then, the trace can be evaluated as the path from the root node to a leaf node optimizing a criterion. See the paper [1] for more details.

Proposed Trace Error Measure

There are three measures between ground truth and tracing algorithm's output that have to be taken into consideration while evaluating trace errors:

Tip distance error is the euclidean distance between the ground truth tip to the trace tip (i.e. the tip found by the algorithm). Trace distance error is the average distance from all the points on the ground truth to all the points on the trace. Length difference is simply the difference between the length of the ground truth and the trace.

The overall metric proposed takes into accounts for all three types of errors and fuse them in a single trace error measure. An important threshold that has to be taken into account in the error measure is 0.792μm which is set to reflect
the maximum error acceptable to biologists.

Results

In total 33 MT tracks on 8 stacks with 1374 MT traces are available for evaluation. The results are shown for the tracing algorithm proposed in [1] with compared to Expert 1. The figure on the left (a) is a graph of all three distance errors for one microtubule over 43 frames. The figure on the right (b) is a graph of the proposed Trace Error for the same microtubule over the same frames. The results shown in Table (c) are quite promising. The first row represents the averaged trace error measure for all the stacks, frames and traces. The follwing rows represent the number of traces that satisfy the error condition bigger than a certain threshold, divided by the number of all traces.We believe that the proposed Trace error does a very good job of summarizing and combining the three key errors. We also believe that it gives a better overall picture of the performance of the algorithm than simply looking at any of the errors in isolation.

(a)	(b)
Trace Error Measure (average) 0.2536 µm Tip Error 0.0840 µm Body Distance Error 0.0855 µm Length Difference Error 0.0780 µm Tip || Body Distance || Length Difference 0.0862 µm (c)

Fused Ground Truth

Four experts provided manual segmentation for 33 MT tracks on 8 stacks with 1374 MT traces. Currently, we are working on how to fuse the multiple ground true in order to obtain a "true ground truth". One possible solution is to estimate the "true ground truth" by connecting the points chosen by the experts that forms the microtubules and fusing the 5 experts segmentations using Warfield's STAPLE algorithm [2]. The fused ground truth is a probabilistic estimate of finding a track at a certain position as shown in the video below. The fused ground truth obtained with the STAPLE algorithm for the 8 stacks can be downloaded here (e.g. Stack 7-13dm6.tif).

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