We propose a linear-time line segment detector that gives accurate results, a controlled number of false detections, and requires no parameter tuning. This algorithm is tested and compared to state-of-the-art algorithms on a wide set of natural images.

LSD is a linear-time Line Segment Detector giving subpixel accurate results. It is designed to work on any digital image without parameter tuning. It controls its own number of false detections: on average, one false alarm is allowed per image [1]. The method is based on Burns, Hanson, and Riseman's method [2], and uses an a contrario validation approach according to Desolneux, Moisan, and Morel's theory [3,4]. The version described here includes some further improvement over the one described in our original article [1]. Source CodeThe ANSI C implementation of LSD version 1.6 is the one which has been peer reviewed and accepted by IPOL. The source code, the code documentation, and the online demo are accessible at the IPOL web page of this article 1 . Supplementary MaterialAlso available at the IPOL web page of this article 2 are two older implementations of LSD, versions 1.0 and 1.5, as well as an example of applying LSD, frame by frame, to a video. The version 1.0 of LSD code corresponds better to the algorithm described in our original article [1], and does not include the further improvements described here and included in the current version; they can be compiled, both, as a C language program or using the Megawave2 3 framework. Versions 1.0 and 1.5 of the code are non reviewed material.

Strategies for the determination of 3D structures of biological macromolecules using electron crystallography and single-particle electron microscopy utilize powerful tools for the averaging of information obtained from 2D projection images of structurally homogeneous specimens. In contrast, electron tomographic approaches have often been used to study the 3D structures of heterogeneous, one-of-a-kind objects such as whole cells where image-averaging strategies are not applicable. Complex entities such as cells and viruses, nevertheless, contain multiple copies of numerous macromolecules that can individually be subjected to 3D averaging. Here we present a complete framework for alignment, classification, and averaging of volumes derived by electron tomography that is computationally efficient and effectively accounts for the missing wedge that is inherent to limited-angle electron tomography. Modeling the missing data as a multiplying mask in reciprocal space we show that the effect of the missing wedge can be accounted for seamlessly in all alignment and classification operations. We solve the alignment problem using the convolution theorem in harmonic analysis, thus eliminating the need for approaches that require exhaustive angular search, and adopt an iterative approach to alignment and classification that does not require the use of external references. We demonstrate that our method can be successfully applied for 3D classification and averaging of phantom volumes as well as experimentally obtained tomograms of GroEL where the outcomes of the analysis can be quantitatively compared against the expected results.

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