Straightening Caenorhabditis elegans images

Abstract

Motivation: Caenorhabditis elegans, a roundworm found in soil, is a widely studied model organism with about 1000 cells in the adult. Producing high-resolution fluorescence images of C.elegans to reveal biological insights is becoming routine, motivating the development of advanced computational tools for analyzing the resulting image stacks. For example, worm bodies usually curve significantly in images. Thus one must 'straighten' the worms if they are to be compared under a canonical coordinate system.

Results: We develop a worm straightening algorithm (WSA) that restacks cutting planes orthogonal to a 'backbone' that models the anterior-posterior axis of the worm. We formulate the backbone as a parametric cubic spline defined by a series of control points. We develop two methods for automatically determining the locations of the control points. Our experimental methods show that our approaches effectively straighten both 2D and 3D worm images.

Fig. 1.

Schematic illustration of WSA. (a) A curved worm image. (b) The detected backbone (red), the respective control points (red dots) and orthogonal cutting lines/planes (purple lines P1 and P2). Also shown is the worm boundary (blue), which is not used in the BDB⁻ algorithm (see Section 3.1) but is used in the faster BDB⁺ algorithm (see Section 3.2). (c) The straightened worm image.

Fig. 2.

Backbone detection using BDB⁻. Different energy terms (plotted in different colors) are used for comparison. (a) Comparison with different energy terms. (b) Results of 10 BDB⁻ backbones (obtained based on 10 random initializations) overlaid together with 20 manually drawn backbones (produced by two subjects).

Fig. 3.

Comparison of backbones detected with and without the smoothness energy term. The less satisfactory regions of the backbone curve are labeled using purple arrows in the zoom-in box.

Fig. 4.

Backbone detection results using different methods. (a) Our BDB⁺ result, where the backbone (green curve and dots) evolves from the MST diameter (red line) produced for a random sub-graph, whose vertexes (150 blue and red dots) are randomly sampled from the entire set of pixel vertexes on the worm body (>80 000 pixels in this image). (b) Morphological image skeleton. (c) Morphological image thinning for the image rotated 30°. (d) The backbone detected using BDB⁻ (red) overlaid with the BDB⁺ backbone (green).

Fig. 5.

Straightening results on a 3D image. Only one z-section is shown. (a) The original worm (25% of the real size), (b) the straighten worm (20% size), (c) tail region of the original worm (80% size) and (d) tail region of the straightened worm (80% size).