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The Flying Cylinder: A New Algorithm for Filament Recognition in Noisy Stereo Images
Abstract
We present a new method of automatic 3D filament representation which uses stereo micrographs to reconstruct three-dimensional trajectories of filament-like objects as DNA molecules. The method deals with low contrasted and noisy images, as obtained from cryovitrified samples by means of electron microscopy. The three-dimensional information is extracted from skeletizing simultaneously both images of a given stereo-pair, instead of processing them separately. The main advantages of the technique are reproducibility and speed, compared to the reconstruction done by manual registration, i.e., clicking on the stereo micrographs.
... The early approaches to this problem included manual reconstruction [91] and a semi-automatic search algorithm called the flying cylinder [92,93]. In the manual scheme, the user clicks on the images to introduce pairs of corresponding points that define the curve; this is time consuming and not necessarily reproducible. ...
... In traditional schemes, these variations are removed by a high-pass preprocessing filter[92]. ...
In this thesis, we present a coherent and consistent approach for the estimation of shape and shape attributes from noisy images. As compared to the traditional sequential approach, our scheme is centered on a shape model which drives the feature extraction, shape optimization, and the attribute evaluation modules. In the first section, we deal with the detection of image features that guide the shape-extraction process. We propose a general approach for the design of 2-D feature detectors from a class of steerable functions, based on the optimization of a Canny-like criterion. As compared to previous computational designs, our approach is truly 2-D and yields more orientation selective detectors. We then address the estimation of the global shape from an image. Specifically, we propose to use cubic-spline-based parametric active contour models to solve two shape-extraction problems: (i) the segmentation of closed objects and (ii) the 3-D reconstruction of DNA filaments from their stereo cryo-electron micrographs. We present several enhancements of existing snake algorithms for segmentation. For the detection of 3-D DNA filaments from their orthogonal projections, we introduce the concept of projection-steerable matched filtering. We then use a 3-D snake algorithm to reconstruct the shape. Next, we analyze the efficiency of curve representations using refinable basis functions for the description of shape boundaries. We derive an exact expression for the error when we approximate a periodic signal in a scaling-function basis. Finally, we present a method for the exact computation of the area moments of such shapes.
... The algorithm is robust and precise because it performs a global optimization. This is in contrast with the more classical approaches such as morphological processing, flying cylinders [4] etc. ...
We propose an algorithm for the 3-D reconstruction of DNA filaments from a pair of stereo cryo-electron micrographs. The underlying principle is to specify a 3-D model of a filament - described as a spline curve - and to fit it to the 2-D data using a snake-like algorithm. To drive the snake, we constructed a ridge-enhancing vector field for each of the images based on the maximum output of a bank of rotating matched filters. The magnitude of the field gives a confidence measure for the presence of a filament and the phase indicates its direction. We also propose a fast algorithm to perform the matched filtering. The snake algorithm starts with an initial curve (input by the user) and evolves it so that its projections on the viewing plane are in maximal agreement with the corresponding vector fields.
... We derive the optimally elongated local template in Appendix A as (23) See 3-D plots of this detector inFig. 4. 6 In traditional schemes, these variations are removed by a high-pass preprocessing filter [5]. Neglecting the normalization constant, we rewrite the expression for the optimal filter (23) oriented along the unit vector as ...
We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we introduce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well.
... All these aspects make the reconstruction problem difficult. The early approaches to this problem included manual recon- struction [2] and a semi-automatic search algorithm called the flying cylinder [3]. The manual scheme is time-consuming and not necessarily reproducible. ...
We introduce a 3-D parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We consider a 3-D filament (consisting of a B-spline skeleton and a specified radial profile) and match its projections with the micrographs using an optimization algorithm. To accelerate the evaluation of the projections, we approximate the global model locally by an elongated blob-like template that is designed to be projection-steerable. This means that the 2-D projections of the template at any 3-D orientation can be expressed as a linear combination of a few basis functions. Thus, the matching of the template projections is reduced to evaluating a weighted sum of the inner-products between the basis functions and the micrographs. We choose an internal energy term that penalizes the total curvature magnitude of the curve. We also use a constraint energy term that forces the curve to have a specified length. The sum of these terms along with the image energy obtained from the matching process is minimized using a conjugate-gradient algorithm. We validate the algorithm using real as well as simulated data.
In vivo the red blood cell reversibly and rapidly deforms as it passes through the small capillaries. Although the physiochemical basis of the red cell's deformability is unknown, it is regarded as being a property of the membrane protein spectrin. We have used cryoelectron microscopy to study the structure of spectrin in membrane skeletons to determine how its molecular structure confers elastic properties on the cell membrane. Cryomicroscopy has the virtue of minimally perturbing easily deformable structures such as spectrin.
Figure 1 is an electron micrograph of a portion of a frozen-hydrated red cell skeleton. The spectrin molecules are indicated by the arrow heads. They cross link the skeletal network by interacting with short rod like segments F-actin (indicated by the arrows) containing about 13 actin molecules. In such micrographs the spectrin appears to have a sinusoidal shape whereas in negatively stained preparations spectrin appears to be straight.
We have used the procedure of Margalef in order to determine the three dimensional trajectory of the spectrin molecule.
Deriving accurate three-dimensional (3-D) structural information of materials at the nanometre level is often crucial for understanding their properties. Tomography in transmission electron microscopy (TEM) is a powerful technique that provides such information. It is however demanding and sometimes inapplicable, as it requires the acquisition of multiple images within a large tilt arc and hence prolonged exposure to electrons. In some cases, prior knowledge about the structure can tremendously simplify the 3-D reconstruction if incorporated adequately. Here, a novel algorithm is presented that is able to produce a full 3-D reconstruction of curvilinear structures from stereo pair of TEM images acquired within a small tilt range that spans from only a few to tens of degrees. Reliability of the algorithm is demonstrated through reconstruction of a model 3-D object from its simulated projections, and is compared with that of conventional tomography. This method is experimentally demonstrated for the 3-D visualization of dislocation arrangements in a deformed metallic micro-pillar.
Information on spatial correlation in the tangent direction along electron microscope images of filamentous molecule is shown to be obtainable by the analysis of statistical fluctuations in curvature, yielding an absolute measure of the persistence parameter amicro. The relationship of amicro, a local, microscopic parameter, to the persistence length introduced by Kratky and Porod is discussed. The hypotheses underlying the assumed theoretical model concern (1) the shape of the angle distribution, assumed to be Gaussian; (2) the passage from a three- to a two-dimensional situation, which is supposed to occur by deformation of the flexible chain in a manner that preserves the memory of the spatial correlation in orientation (except for the blocking of one degree of freedom); and (3) the adsorption conditions, which should meet the equilibrium requirement as closely as possible. The analytical method has been checked on computer simulated “Gaussian” molecules: the study of the simulated sample was essential in solving the problems connected with minimum statistics requirements and the effect of the reading error. Experimental images obtained for T2 DNA fragments at different ionic strengths by Kleinschmidt's adsorption technique have been analyzed by means of an automatic flying spot digitizer, the “Precision Encoder and Pattern Recognition.” The results show that adsorbed molecules do in fact “remember” the rigidity they possessed in solution and that the Gaussian hypothesis is well verified. Consequently, the slopes of log cosθ(l) or θ2(l) may be used indifferently in the estimate of amicro. The dependence of this parameter on ionic strength in the range explored shows the expected behavior.
Axial deflection of DNA molecules in solution results from thermal motion and intrinsic curvature related to the DNA sequence. In order to measure directly the contribution of thermal motion we constructed intrinsically straight DNA molecules and measured their persistence length by cryo-electron microscopy. The persistence length of such intrinsically straight DNA molecules suspended in thin layers of cryo-vitrified solutions is about 80 nm. In order to test our experimental approach, we measured the apparent persistence length of DNA molecules with natural "random" sequences. The result of about 45 nm is consistent with the generally accepted value of the apparent persistence length of natural DNA sequences. By comparing the apparent persistence length to intrinsically straight DNA with that of natural DNA, it is possible to determine both the dynamic and the static contributions to the apparent persistence length.
Emphasis has been recently given to automatic segmentation of vascular network observed by means of Digital Subtraction Angiography. This paper details a new algorithm which determines the medial axes and the contours of the vessesl in the whole vascular tree.
An image analysis method is presented which allows for the reconstruction of the three-dimensional path of filamentous objects from two of their projections. Starting with stereo pairs, this method is used to trace the trajectory of DNA molecules embedded in vitreous ice and leads to a faithful representation of their three-dimensional shape in solution. This computer-aided reconstruction is superior to the subjective three-dimensional impression generated by observation of stereo pairs of micrographs because it enables one to look at the reconstructed molecules from any chosen direction and distance and allows quantitative analysis such as determination of distances, curvature, persistence length, and writhe of DNA molecules in solution.
This chapter discusses the cryoelectron microscopy of vitrified specimens to observe the specimen with all its water immobilized by low temperature, the cooling being done in such a way that water has no time to crystallize. The native structure of macromolecules in solution is, therefore, essentially preserved. Forming a very thin layer of liquid for vitrification means that the surface-to-volume ratio must be very large. This is an energetically unfavorable situation. In practice, this means that the liquid film tends to be too thick for electron microscopy, or it dries nearly instantaneously when it has the desired thickness. It was difficult to develop a supporting film with surface properties stabilizing the adsorbed liquid film. In the electron microscope, the vitrified specimen must be kept at a low temperature. This can be achieved in a conventional electron microscope equipped with a simple cryospecimen holder. The required temperature of 160° is obtained by convenient nitrogen cooling. A sophisticated electron microscope or the very low temperature that can be provided by helium is of little advantage. The only special feature that must be incorporated is an efficient anticontaminator.
The three-dimensional reconstruction of vascular trees from a very limited number of two-dimensional projections is an active research field. The quality of the results (resolution in terms of vessel size and geometrical location) is highly dependent on the overall distortions introduced in the data acquisition process but is also related to the reliability of feature detection. A new approach based on mathematical morphology is proposed in this paper for extracting the centrelines and edges of coronary vessels from digital subtracted angiograms. These results are compared with those from an alternative method based on vectorial tracking and a directed contour finder.
Analyse d'Images d'ADN par Extraction de Con-tours et Morphologie Mathematique
- A Poncet
Poncet, A. (1990) Analyse d'Images d'ADN par Extraction de Con-tours et Morphologie Mathematique, Travail de diplô, Lab-oratoire de Traitement des Signaux, Swiss Federal Institute of Technology, Lausanne, Switzerland.