Detection of Filamentous Structures in Low-Contrast Images Acquired in Defocus Pair by Cryo-Electron Microscopy

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1 Detection of Filamentous Structures in Low-Contrast Images Acquired in Defocus Pair by Cryo-Electron Microscopy Yuanxin Zhu, Bridget Carragher, David Kriegman and Clint S. Potter (Submitted to IEEE Computer Society Conf. Computer Vision and Pattern Recognition, Hawaii) Date Issued: June 2001 The Beckman Institute Imaging Technology Group Technical Report Copyright 2001 Board of Trustees of the University of Illinois The Beckman Institute for Advanced Science and Technology Imaging Technology Group 405 N Mathews Urbana, IL techreports@itg.uiuc.edu

2 Detection of Filamentous Structures in Low-Contrast Images Acquired in Defocus Pair by Cryo-Electron Microscopy Yuanxin Zhu, Bridget Carragher, # David Kriegman, and Clinton S. Potter Beckman Institute, and # Department of Computer Science, University of Illinois, Urbana, Illinois Abstract Since the foundation of the three-dimensional image reconstruction of helical objects from electron micrographs was laid more than 30 years ago, there have been sustained developments in specimen preparation, data acquisition, image analysis, and interpretation of results. However, the boxing of filaments in large number of images one of the critical step toward the reconstruction in atomic resolution is still restrained by manual processing even though interactive interfaces have been built to aid the tedious and less accurate manual boxing. This article describes an accurate approach for automatically detecting filamentous structures in lowcontrast images acquired in defocus pair using cryoelectron microscopy. The performance of the proposed approach has been evaluated across various magnifications and a series of defocus values using as a test driver specimens of tobacco mosaic virus (TMV) preserved in vitreous ice. By integrating the proposed approach into our automated data acquisition and reconstruction, we are able to get a 3D map of TMV at the resolution of 10Å within hours in a fully automatic way. 1. Introduction The next decade promises to be an exciting one for understanding the inner workings of the cell. Genomes are being sequenced at an ever-increasing pace, and protein expression systems are being perfected, so we can expect that many of the polypeptide building blocks of the cell will be available for detailed study soon. It is clear that the majority of a cell s proteins do not function alone but are rather organized into macromolecular complexes. These complexes can be thought of as machines containing functional modules (the enzymatic core), regulatory modules (controlling the core), and localization modules (directing the complex to a particular part of the cell). Examples include microtubule-motor complexes, actomyosin, nuclear pore complexes, nucleic acid replication and transcription complexes, vaults, ribosomes, proteosomes, etc. Cryo-electron microscopy (Cryo-EM) is an approach that can be used to provide valuable structural information on such complexes. Briefly, the technique uses a transmission electron microscope (TEM) to acquire 2D projection images of a specimen preserved in vitreous ice, allowing the specimen to be examined in its native state [1]. A 3D electron density map can be reconstructed from the 2D projections using what are essentially tomographic reconstruction techniques. The particular technique is dictated by the symmetry and geometry of the specimen. Cryo-EM as a technique does however suffer from one serious drawback it is very time consuming and much of the work requires manual data processing and is extremely tedious. One of the principal bottlenecks to this technique is the enormous number of images that must be acquired for the structural analysis. This requirement results from the necessity for using extremely low doses of electrons (10e/A^2) to image the specimen in order to avoid beam induced radiation damage. As a result the acquired images have a very low signal to noise ratio, and in order to reconstruct a 3D electron density map a very large number of images must be averaged together. The exact number of images required to complete a 3D reconstruction of a macromolecule depends on its size and on the desired resolution. It is generally agreed that in order to interpret a structure to atomic resolution, data from possibly hundreds of thousands of copies of the macromolecule must be used [2]. This in turn requires the collection of thousands to tens of thousands of electron micrographs. One of the current constraints in the field is the manual data acquisition methods that are slow and labor-intensive, and result in sometimes low percentages of suitable images. This is where we have demonstrated that techniques from computer vision have proven to be extremely effective and are opening the door to rapid advances in experimental structural biology. The paper describes how these techniques are used to solve a specific aspect, and in turn informs the computer vision and pattern recognition community of new opportunities for applying vision methods within a new domain. One could compare the state of molecular microscopy today to the situation in the x-ray crystallography field some 20 years ago. Since then the x-ray crystallographers have expended a great deal of effort on automating the time consuming and tedious aspects of their work. The result is that today x-ray structure determinations can be done fast and efficiently as evidenced by the veritable explosion of new structures appearing in the journals. Cryo-EM is ready for a similar developmental effort.

3 Using helical objects as the driver, we have been developing an integrated system for cryo-em that would allow a 3D electron density map to be automatically generated within hours of a specimen being inserted in the microscope with no manual intervention. This would vastly improve both the quality and quantity of data collection and processing. Towards this goal, we have already automated acquiring images from the electron microscope [3,4]. The system performs all the operations normally performed by an experienced microscopist including multi-scale image analysis to identify suitable targets for high magnification image acquisition. The system can acquire up to 1000 images a day and the overall performance is equivalent to that of an experienced microscopist. More than 30 years ago, DeRosier and Moore [5] laid the foundation for the 3D reconstruction of biological structures with helical symmetry from electron micrographs. Since then, tools have been developed to aid the image processing of helical objects [6-15]. Although interactive interfaces (for example, the IMGBOX [15]) have been built for extracting (boxing out regions of) filaments in images where multiple filaments at various orientation and length may present, they are essentially manual limited both in speed and accuracy. Integration of the automated data acquisition with the 3D reconstruction process requires an automatic boxing process, i.e. for identifying helical filaments in projection images. This automation is particularly promising since the boxing step is often the bottleneck for high-resolution reconstruction [16]. To our best knowledge, no such technique has been reportedsofar. This paper presents an accurate approach for automatically detecting filamentous structures in lowdose, low-contrast images acquired in defocus pair using cryo-em; the first image is acquired at very near to focus (NTF) condition (e.g., -0.3 ~ -0.15µm, - and + indicate under-focus and over-focus respectively) and the second one at a farther from focus (FFF) (e.g., -3 ~ - 2µm), see Fig. 2, for example. The time interval between the two exposures is less than 1s. There are at least two major advantages of using a defocus pair of images. First, by combining the two images in the defocus pair, relatively high contrast at both low and high spatial frequencies can be attained. Second, the moderately strong low-resolution signals in the FFF images make it possible for us to develop algorithms to identify filamentous structures automatically. The idea of using a defocus pair of images has been explored by several other researchers [17-20]. Our approach begins with a three-level perceptual organization algorithm to detect filaments in the FFF images, see Fig. 1 for a schematic overview. Because the NTF images are acquired very close to focus (e.g µm), the contrast in such images is extremely low. On the other hand, the NTF image in a defocus pair covers the same specimen area as the FFF image. The relative distance between filaments within the NTF image should be the same as that of the FFF image. We therefore circumvent directly spotting filaments in the NTF image and instead detect filaments in the FFF image which is then aligned using phase correlation techniques with the NTF image. After alignment, the filaments are extracted from the NTF image using the coordinates identified in the FFF image. High magnification images in defocus pair; a very near-to-focus (NTF) image is acquired first, followed by a far-from-focus (FFF) image from any chosen specimen area. Detection of filaments in the FFF image using a three-level perceptual organization Edge detection Discontinuous edges grouped into line segments Line segments organized into filaments Alignment of the NTF image to the FFF image Extraction of filaments in NTF image using coordinates as identified in the FFF image Figure 1. Schematic overview of the automated filament finding approach. The performance of the proposed approach was tested and evaluated by applying it to high magnification micrographs of tobacco mosaic virus preserved in vitreous ice. Performance is assessed in terms of the percentages of correctly identified filaments, false alarms (incorrectly identified areas), and false dismissals (unboxed filaments). The calculation is based on a comparison to the filaments that would have been selected by an expert. False dismissals do not constitute a serious type of error as long as there are many filament images available and the percentage of falsely dismissing is low. False alarms do

4 pose a severe error since they are not projections of real helical filaments and thus introduce significant error into the reconstruction process. Therefore, a preferred filament detection approach should produce a high percentage of correctly identified filaments while maintaining a very low percentage of false alarms. 2 Materials and Methods 2.1 Image acquisition Our automated acquisition system [3, 4] was used to record high magnification images of helical filaments of tobacco mosaic virus (TMV) preserved in vitreous ice. TMV is a well-characterized helical virus [21]. It is often used as a transmission electron microscopy (TEM) standard for calibration of magnification and determining resolution and provides an ideal test specimen for evaluating a new technique. Defocus pairs of images were collected using a Philips CM200 TEM quipped with a 1Kx1K CCD camera with phospor scintillator. At this magnification the pixel size was 2.8Å and the accumulated dose for any chosen specimen area was about 10e/A^2. An example of a defocus pair of images acquired in this way is shown in Fig. 2(a) and (b). The images shows projections of TMVs. These structures form helical filaments 18 nm in diameter and 300 nm in length. (a) (c) (b) (d) Figure 2. Illustration of filament finding in a defocus pair of images of specimens of tobacco mosaic virus (TMV) (6,6000x) acquired using cryo-electron microscopy (EM). The image shown in (a) was acquired first at a very near-tofocus (NTF) condition (-0.3µm) and the one shown in (b) was recorded second at much farther from focus (FFF) (-3µm). Following filament finding in the FFF image, alignment of the NTF image to the FFF image results in 7 filaments found in the pair of images shown in (c) and (d) respectively where targeted filaments outlined by pairs of parallel line segments. 2.2 Introduction to perceptual organization In humans, perceptual organization is the ability to immediately detect relationships such as collinearity, parallelism, connectivity, and repetitive patterns among image elements [22]. Researchers in human visual perception, especially the Gestalt psychologists [23,24], have long recognized the importance of finding organization in sensory data. The Gestalt law of organization states the common rules by which our visual system attempts to group information [23,24]. Some of these rules include proximity, similarity, common fate, continuation and closure. In computer vision, as Mohan and Nevatia [25] proposed, perceptual organization takes primitive image elements and generates representations of feature groupings that encode the structural interrelationships between the component elements. Many perceptual grouping algorithms [25-28] have been proposed, and surveys of these works can be found [22, 29-31]. 2.3 Detecting filaments in FFF images We will model the filament detection process in the FFF images as a three-level perceptual organization based on the terminology proposed by Sarkar and Boyer [30] who arrange the features to be organized into four categories: signal, primitive, structural, and assembly. At each level, feature elements that are not grouped into higher-level features are discarded. Briefly, at the signal level, a Canny edge detector [32] is used to detect weak filament boundaries. A Hough transform [33] followed by detecting end points of line segments and merging collinear line segments is developed at the primitive level to organize discontinuous edges into line segments with a complete description. At the structural level, line segments are grouped into filamentous structures, areas enclosed by pairs of straight lines, by seeking parallelism and utilizing high-level knowledge. In addition, statistical evidence is used to separate two filaments if they are joined together end to end. Edge detection For noisy images, it is necessary that at the signal level, edge detection be used to enhance lowlevel feature elements by organizing interesting boundary points into edge chains and suppressing the possible effects of noise on higher-level perceptual organization. Edge detection is typically a three-step process including

5 noise smoothing, edge enhancement and edge localization [34]. We adopt probably the most widely used edge detector in today s machine vision community, the Canny edge detector, to detect these weak boundaries. Selecting the input parameters of the Canny algorithm is a critical step because the resulting edge quality varies greatly with the choice of parameters. At the signal level, the input parameters were selected to optimize the quality of edges for the purpose of higher-level perceptual organization. The best single overall parameter set for the Canny edge detector, identified by the performance measure method and evaluated on a wide variety of real images [35], does not produce a successful result as applied to images in our case, see Fig. 3, for example. To select the input parameters suitable for our highly noisy, low-contrast cryo-em images, we first select a range of parameters that samples the space broadly enough but not too coarsely for each parameter, and then chose the best suitable input parameter by visual inspection of the resulting edge images. While this selection does not guarantee that optimal input parameter set was identified, it does generate good results in a timely way. Fig. 3 (a) and (b) show the edges detected using different parameter set. Line detection and end points computing At the primitive level, the Hough transform (HT), followed by searching end points of the line segments and merging collinear line segments, is used to organize noisy and discontinuous edges into complete line segments. To simplify the computation, the ρ θ rather than slopeintercept parameters are used to parameterize lines [36]. The use of the HT to detect lines in an image involves the computation of HT for each pixel in the image, accumulating votes in a two dimensional accumulator array and searching the array for peaks holding information of potential lines present in the image. The accumulator array becomes complicated when the image contains multiple lines, with multiple peaks, some of which may not correspond to lines but are artifacts of noise in the image. Therefore, we iteratively detect the dominant line in the image, remove its contribution from the accumulator array, and then repeat to find the dominant of the remaining lines. The peaks in the accumulator array provide only the shortest distance of the line to origin ( ρ ) and the angle that the normal makes with the x-axis (θ )oftheimage plane. They fail to provide any information regarding the length, position, or end points of the line segments, which are vital to the detection of acceptable filaments. Several algorithms have been proposed in the literature for finding the length and end points of a line from the Hough accumulator array [37-39]. The drawback of these algorithms is that they are computationally intensive. Our integrated system requires that the computation be performed on the order of seconds to maximize throughput. We extend an algorithm, due to McLaughlin and Alder [40], for computing the end points of a line segment directly from the image, based on accurate line parameters detected by HT. Accurate line parameters can be detected by using HT since most noise has been removed by the edge detection process. At each iteration, we find the global maximum in the accumulator array and from this compute the equation (parameters) of the corresponding line. A simple post-processing step is used to find the beginning and end points of the line, which involves moving a small window (e.g pixels) along the line and counting the number of edge pixels in the window. This count will rise above a threshold value at the beginning of the line and decrease below the threshold at the line end. Collinear line segments are merged by allowing gaps in the line segment while moving the small window along the line. Having found two end points of the line segment, we next tag all pixels lying on the line segment and remove the contribution of these pixels to the Hough accumulator array. The Hough accumulator array is now becoming equivalent to that of an image that had not contained the detected line segment. The above processing is repeated with the new global maximum of the accumulator array. This continues until the maximum is below a threshold value which, found from experimentation, is recalculated at each iteration. Edges that are not grouped into line segments are discarded after primitive-level perceptual organization. Fig. 3(c) shows an example of the line segments with acceptable length obtained by primitivelevel perceptual organization where we can see that the end points of those line segments were accurately identified and collinear line segments were successfully merged. Detection of filamentous structures At the structural level, line segments are actively grouped into filaments by seeking parallelism and employing knowledge obtained from training data. A filament is the area enclosed by two line segments with a particular structural relationship. Besides parallelism, the two line segments should also meet some heuristics: (i) The distance between the two line segments should be between specified maximal and minimal values, both of which are determined by statistical analysis on training data. (ii) The shorter one of the two line segments should be no less than one third of the length of the longer line segment. (iii) There should be some overlapped area between the two line segments. The overlapped area can be measured from the correspondence between the end points of the two line segments. At least one third of either one should overlap with the other line segment. The area enclosed by two line segments that meet these requirements is considered as a possible filament. Finding every possible filament requires that the

6 algorithm search for all possible matches in a neighborhood of each line segment. As a result, there may be situations where a line segment has multiple matches (filaments). In this case, the match with the largest overlapped area wins the competition. Therefore, each line segment can be a boundary of only one filament. Like the ungrouped edges in the primitive-level, unmatched line segments are discarded. (a) (c) (d) (b) Figure 3. Illustration of filament finding in the FFF image of a defocus pair using a three-level perceptual organization algorithm. (a) and (b) Edges detected in the image, shown in Fig. 2(b), using the parameter set identified by Heath et al. [35] and that we selected, respectively. (c) Line segments with acceptable length obtained by the primitive-level perceptual organization. (d) 7 filaments were detected after structural-level organization. In selecting filaments from the images that will be passed to the 3D reconstruction algorithms, more stringent constraints must be used to limit the number of filaments in order for the reconstruction process to be accurate and efficient. First, only the area enclosed by the overlapped part of the two line segments are clipped as the detected filament. Secondly, as described earlier, filaments may be joined end to end along their length (see Fig. 4(a), for example) and must be individually segmented prior to the 3D image reconstruction. Thus our algorithm must separate a filament aggregation into multiple segments if it consists of two or more filaments that are joined together end to end (the longest filament in the image shown in Fig. 3(e), fox example). Finally, filaments that are shorter than the minimal length required for further analysis are discarded. Separation of end-to-end joins To detect whether a filament actually consists of two or more shorter filaments that are end-to-end joined together, we have adopted a four-step approach. (i) Rotate the image around its center so that the inclined filament becomes horizontal, and then cut the filament out of the rotated image. (ii) Enhance possible end-to-end joins by linearly filtering the filament image with a Gaussian kernel and computing the gradient magnitude for each pixel in the smoothed image. (iii) Sum along the columns of the image to generate a 1D projection in which the global peak corresponds to the position of a possible end-to-end join. (iv) Determine the location of the end-to-end joins by thresholding based on the statistics (maxium, mean, and standard deviation) of the 1D projection. Using this method the end-to-end join was identified in Fig. 4(a) and the longest filament as shown in Fig. 4(b) is extracted for further analysis. After examining a set of filament images, we found that the metric defined as ( m µ ) W can be used to accurately discriminate whether a filament contains endto-end joins, where m and µ are, respectively, the maximum and the mean of the 1D projection, and W is the width of the filament. First, a threshold value is learned from the set of images by visual inspection. Then a filament is classified as one containing one or more endto-end joins if the value of the metric is larger than the threshold value and the filament will be separated along the position indicated by the global peak in the 1D projection. A recursive approach is used when there are multiple end-to-end joins within one filament. In other words, a filament is split into two sub-filaments along its dominant split point indicated by the global peak in the 1D projection. The sub-filaments are examined using the same approach, split them if there are end-to-end joins, repeat this process until all filaments do not contain any end-to-end join. (a) (b) Figure 4. Illustration of end-to-end separation. (a) An extracted region from the image, shown in Fig. 2(d), represents two filaments aggregated end to end as indicated by the arrow. (b) The longest filament in (d) after separation along the end-to-end join.

7 2.4 Detecting filaments in NTF images As mentioned earlier, one of the advantages of image acquisition in defocus pair is to use information about filaments in the FFF image of the defocus pair to aid filament finding in the NTF image of the pair. We first align the NTF images to their corresponding FFF images then extract filaments in the NTF images using the coordinates as identified in the corresponding FFF images. An example of a pair of NTF and FFF images with 7 filaments successfully targeted in each image is shown in Fig. 2. Cross-correlation has been the most widely exploited tool for aligning pairs of images acquired under different conditions [41]. The cross-correlation function (CCF) is usually calculated by first forming the cross power spectrum (the product of multiplying the complex conjugate of the Fourier transform of the first image by the transform of the second) and then inverse-transforming the cross power spectrum back to real space. Ideally, the CCF exhibits a well-posed local peak, the position of which indicates the relative displacement of the two images. However, as [42] observed, the cross-correlation peak deteriorates rapidly with increasing defocus difference between a pair of images. Our initial experiment confirmed that the peak shape of the CCF between a pair of NTF and FFF images is generally unrecognizable (see Fig. 5 (a)). (a) (b) Figure 5. The phase correlation and crosscorrelation surfaces obtained from the defocus pairs of images shown in Fig. 2(a) and (b). The peak (indication of relative displacement of the two images) on the phase-correlation surface is much sharper than that on the cross-correlation surface. In order to improve the peak shape of the CCF under noise or strong background variations, several variants involving linear or non-linear modification in Fourier space has been previously proposed (for review, see [43]). Particularly, Saxton [43] proposed two modifications for accurately aligning sets of images. The first modification, called a phase-compensated CCF, was supposed to address general case, when the transfer functions with which the images have been recorded are arbitrarily complex, but requires at least an approximate knowledge of the transfer functions in force. The second modification, proposed particularly for axial imaging with contrast dominated either by phase or amplitude as is true in our case, does not require any knowledge of the transfer functions, called a phase-doubled CCF [43]. The phasedoubled CCF is calculated as the inverse Fourier transform of the phase difference between two images (the cross power spectrum of the two images divided by its modulus). We noticed interestingly that the phasedoubled CCF is essentially the same as the phase correlation alignment method developed by Kuglin and Hines [44]. As indicated by the latter, the phase correlation is a highly accurate alignment technique that exhibits an extremely narrow correlation peak (see Fig. 4(b), for example) and is generally insensitive to narrow bandwidth noise and conventional image degradations. We therefore adopt the phase correlation technique to align pairs of defocus images. In summary, the algorithm for aligning a defocus pair of images using the phase correlation technique consists of four steps: (i) A 2D fast Fourier transform is computed for the NTF and FFF images which have the same dimensions, resulting in two complex arrays. (ii) The phase difference matrix is derived by forming the cross power spectrum and dividing by its modulus. (iii) The phase correlation function (PCF) is then obtained as a real array by taking the inverse FFT of the phase difference matrix. (iv) The relative displacement of the two images is finally determined by searching the position of the highest peak in the PCF. In general, the position of PCF surface peak is a continuous function of image displacement. Since the PCF surface peak is very sharp, it should be straightforward to measure subpixel (non-integer) displacements through the use of interpolation with a few data points around the peak. In our case, it is accurate enough to align a defocus pair of images by finding an integer displacement between the two images (see Fig. 2(c), for example). 3. Experiment result and analysis We have tested and evaluated the performance of the proposed approach by applying it to high magnification images of helical filaments of tobacco mosaic virus (TMV) acquired under different conditions. As mentioned in the introduction, the performance of the proposed approach is measured in terms of the percentages of correctly identified filaments, false dismissals and false alarms, as compared to the filaments that would have been selected by an experienced user. Table 1 summarizes the overall performance of the proposed approach as applied to the detection of TMV filaments during 3 independent acquisition sessions. Training data was obtained from 141 high magnification images collected in a separate session. The training data is used to derive high-level knowledge,

8 such as range of filament width in pixels, threshold for determining parallelism of two line segments, and so on, which is required by our grouping algorithms. The total number of filaments in each session, listed in Table 1, was visually counted by one of the authors. Table 1 indicates that on average ninety-two percent of TMV filaments can be automatically detected with a very low false alarm rate (lower than four percent, shown in the last row of the Table). There are still a certain number of false dismissals (lower than eight percent, see Table 1). However, while we would like to reduce the false dismissals, the yield is currently sufficient to produce a 3D map during a single data acquisition session. Thus we have achieved the immediate goal of fully automatic filament detection from images acquired in defocus pair using cryo-electron microscopy. Table 1. Performance of the proposed approach measured in 3 independent sessions. Session No Avg. Magnification (x) 66K 66K 88K Image acquisition cond. Average dose (e/a^2) Defocus value for NTF images (µm) Defocus value for FFF images (µm) Number of defocus pairs of images Total number of filaments Correctly detected filaments (%) False dismissals (%) False alarms (%) Summary and concluding remarks The paper presents an accurate approach for automatic identification of filamentous structures in low-dose, lowcontrast images acquired in defocus pair by cryo-electron microscopy. A defocus pair consists of a near-to-focus (NTF) image acquired first followed by a far-from-focus (FFF) image. A three-level perceptual organization algorithm is developed to successfully detect filaments in the FFF image. At each level, feature elements that are not grouped into higher-level features are discarded. At the signal level, edges (mostly filament boundaries) distorted by strong noise are detected using the Canny edge detector. At the primitive level, collinear discontinuous edges are organized into line segments with a complete description using the Hough transform followed by detecting end points of line segments. At the structural level, line segments are grouped into filamentous structures, the area enclosed by a pair of line segments, by seeking parallelism and exploiting high-level knowledge obtained from training data. In the case of two filaments joining together end to end, a statistical method is used to accurately locate the splitting boundary and thus separate them along the boundary. Finally, the NTF image is aligned to the FFF image using the phase correlation technique and filaments in the NTF image are delineated at the same coordinates identified in the FFF image. The performance of the proposed approach has been tested and evaluated by applying it to high magnification images of helical specimens preserved in vitreous ice, particularly the tobacco mosaic virus (TMV). Experimental result indicates that on average over ninetytwo percent of a large number of filaments can be accurately detected by the proposed approach with a low percentage of false dismissals and a very low percentage of false alarms, which is desirable for the purpose of structural reconstruction. The yield is currently sufficient to produce a 3D map during a single data acquisition session. In contrast with the conventional crosscorrelation the result of the phase correlation alignment exhibits a much shaper correlation peak. Using the phase correlation technique, the alignment between defocus pairs, where there are filaments selected in the FFF images, can be achieved with almost 100% accuracy. The proposed systemic practical approach for automatic detection of filamentous structures should not only facilitate the three-dimensional reconstruction of helical objects for cryo-electron microscopy, but also expedites automated electron microscopy. In our efforts toward high throughput automated electron microscopy, we are next working on exploring machine learning techniques for automatic selection of good quality filaments (for the purpose of reconstruction) from the output of the automatic detection stage. We thus need to develop quantitative ways to measure image quality of the filaments. Acknowledgements The authors gratefully acknowledge Jim Pulokas and the rest of the Leginon team at the Beckman Institute for collecting the data and Ron Milligan at The Scripps Research Institute for providing the TMV specimen. This project is supported by NSF (DBI , DBI ) and NIH (GM ). References [1] Dubochet, J., Adrian, and et al. (1988) Cryoelectron mciroscopy of vitrified specimens, Quart. Rev. Biophys. 21, [2] Henderson, R. (1995) The potential and limitations of neutrons, electrons, and X-rays for atomic resolution microscopy of unstained biological macromolecules, Quart. Rev. Biophys. 28,

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