Connectivity-Enforcing Hough Transform for the Robust Extraction of Line Segments

Global voting schemes based on the Hough transform (HT) have been widely used to robustly detect lines in images. However, since the votes do not take line connectivity into account, these methods do not deal well with cluttered images. In opposition, the so-called local methods enforce connectivity but lack robustness to deal with challenging situations that occur in many realistic scenarios, e.g., when line segments cross or when long segments are corrupted. In this paper, we address the critical limitations of the HT as a line segment extractor by incorporating connectivity in the voting process. This is done by only accounting for the contributions of edge points lying in increasingly larger neighborhoods and whose position and directional content agree with potential line segments. As a result, our method, which we call STRAIGHT (Segment exTRAction by connectivity-enforcInG HT), extracts the longest connected segments in each location of the image, thus also integrating into the HT voting process the usually separate step of individual segment extraction. The usage of the Hough space mapping and a corresponding hierarchical implementation make our approach computationally feasible. We present experiments that illustrate, with synthetic and real images, how STRAIGHT succeeds in extracting complete segments in several situations where current methods fail.Comment: Submitted for publicatio

Estimating Epipolar Geometry With The Use of a Camera Mounted Orientation Sensor

Context: Image processing and computer vision are rapidly becoming more and more commonplace, and the amount of information about a scene, such as 3D geometry, that can be obtained from an image, or multiple images of the scene is steadily increasing due to increasing resolutions and availability of imaging sensors, and an active research community. In parallel, advances in hardware design and manufacturing are allowing for devices such as gyroscopes, accelerometers and magnetometers and GPS receivers to be included alongside imaging devices at a consumer level. Aims: This work aims to investigate the use of orientation sensors in the field of computer vision as sources of data to aid with image processing and the determination of a scene’s geometry, in particular, the epipolar geometry of a pair of images - and devises a hybrid methodology from two sets of previous works in order to exploit the information available from orientation sensors alongside data gathered from image processing techniques. Method: A readily available consumer-level orientation sensor was used alongside a digital camera to capture images of a set of scenes and record the orientation of the camera. The fundamental matrix of these pairs of images was calculated using a variety of techniques - both incorporating data from the orientation sensor and excluding its use Results: Some methodologies could not produce an acceptable result for the Fundamental Matrix on certain image pairs, however, a method described in the literature that used an orientation sensor always produced a result - however in cases where the hybrid or purely computer vision methods also produced a result - this was found to be the least accurate. Conclusion: Results from this work show that the use of an orientation sensor to capture information alongside an imaging device can be used to improve both the accuracy and reliability of calculations of the scene’s geometry - however noise from the orientation sensor can limit this accuracy and further research would be needed to determine the magnitude of this problem and methods of mitigation

Computing motion in the primate's visual system

Computing motion on the basis of the time-varying image intensity is a difficult problem for both artificial and biological vision systems. We will show how one well-known gradient-based computer algorithm for estimating visual motion can be implemented within the primate's visual system. This relaxation algorithm computes the optical flow field by minimizing a variational functional of a form commonly encountered in early vision, and is performed in two steps. In the first stage, local motion is computed, while in the second stage spatial integration occurs. Neurons in the second stage represent the optical flow field via a population-coding scheme, such that the vector sum of all neurons at each location codes for the direction and magnitude of the velocity at that location. The resulting network maps onto the magnocellular pathway of the primate visual system, in particular onto cells in the primary visual cortex (V1) as well as onto cells in the middle temporal area (MT). Our algorithm mimics a number of psychophysical phenomena and illusions (perception of coherent plaids, motion capture, motion coherence) as well as electrophysiological recordings. Thus, a single unifying principle ‘the final optical flow should be as smooth as possible’ (except at isolated motion discontinuities) explains a large number of phenomena and links single-cell behavior with perception and computational theory

Shape from periodic texture using the eigenvectors of local affine distortion

This paper shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization, We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery

Common lines ab-initio reconstruction of D2D_2-symmetric molecules

Cryo-electron microscopy is a state-of-the-art method for determining high-resolution three-dimensional models of molecules, from their two-dimensional projection images taken by an electron microscope. A crucial step in this method is to determine a low-resolution model of the molecule using only the given projection images, without using any three-dimensional information, such as an assumed reference model. For molecules without symmetry, this is often done by exploiting common lines between pairs of images. Common lines algorithms have been recently devised for molecules with cyclic symmetry, but no such algorithms exist for molecules with dihedral symmetry. In this work, we present a common lines algorithm for determining the structure of molecules with $D_{2}$ symmetry. The algorithm exploits the common lines between all pairs of images simultaneously, as well as common lines within each image. We demonstrate the applicability of our algorithm using experimental cryo-electron microscopy data