Estimation of Epipolar Geometry via the Radon Transform

One of the key problems in computer vision is the recovery of epipolar geometry constraints between different camera views. The majority of existing techniques rely on point correspondences, which are typically perturbed by mismatches and noise, hence limiting the accuracy of these techniques. To overcome these limitations, we propose a novel approach that estimates epipolar geometry constraints based on a statistical model in the Radon domain. The method requires no correspondences, explicit constraints on the data or assumptions regarding the scene structure. Results are presented on both synthetic and real data that show the method's robustness to noise and outliers

Correspondenceless Structure from Motion

We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions

Radon-based Structure from Motion Without Correspondences

We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. We assume a similarity function defined on the crossproduct of two images which assigns a weight to all feature pairs. This similarity function is integrated over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to filtering the similarity function with a Dirac function embedding the epipolar constraint. The result of this convolution is a function of the five unknownmotion parameters with maxima at the positions of compatible rigid motions. The breakthrough is in the realization that the Radon transform is a filtering operator: If we assume that images are defined on spheres and the epipolar constraint is a group action of two rotations on two spheres, then the Radon transform is a convolution/correlation integral. We propose a new algorithm to compute this integral from the spherical harmonics of the similarity and Dirac functions. The resulting resolution in the motion space depends on the bandwidth we keep from the spherical transform. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions. The algorithm has been tested in sequences of real omnidirectional images and it outperforms correspondence-based structure from motion

Planar Ego-Motion Without Correspondences

General structure-from-motion methods are not adept at dealing with constrained camera motions, even though such motions greatly simplify vision tasks like mobile robot localization. Typical ego-motion techniques designed for such a purpose require locating feature correspondences between images. However, there are many cases where features cannot be matched robustly. For example, images from panoramic sensors are limited by nonuniform angular sampling, which can complicate the feature matching process under wide baseline motions. In this paper we compute the planar ego-motion of a spherical sensor without correspondences. We propose a generalized Hough transform on the space of planar motions. Our transform directly processes the information contained within all the possible feature pair combinations between two images, thereby circumventing the need to isolate the best corresponding matches. We generate the Hough space in an efficient manner by studying the spectral information contained in images of the feature pairs, and by re-treating our Hough transform as a correlation of such feature pair images

Scale-invariant representation of light field images for object recognition and tracking

Achieving perfect scale-invariance is usually not possible using classical color image features. This is mostly because of the fact that a traditional image is a two-dimensional projection of the real world. In contrast, light field imaging makes available rays from multiple view points and thus encodes depth and occlusion information which are very crucial for true scale-invariance. By studying and exploiting the information content of the light field signal and its very regular structure we came up with a provably efficient solution for extracting scale-invariance feature vector representation for more efficient light field matching and retrieval among various views. Our approach is based on a novel integral transform which maps the pixel intensities to a new space in which the effect of scaling can be easily canceled out by a simple integration. The experiments we conducted on various real and synthetic light field images verify that the performance of the proposed approach is promising in terms of both accuracy and time-complexity. As a probable future improvement, incorporating invariance to various other transforms such as rotation and translation will make the algorithm far more applicable

Rotation Recovery from Spherical Images without Correspondences

This paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence. The method is particularly useful for the alignment of large rotations and has potential impact on 3D shape alignment. The foundation of the method lies in the fact that the spherical harmonic coefficients undergo a unitary mapping when the original image is rotated. The correlation between two images is a function of rotations and we show that it has an SO(3)-Fourier transform equal to the pointwise product of spherical harmonic coefficients of the original images. The resolution of the rotation space depends on the bandwidth we choose for the harmonic expansion and the rotation estimate is found through a direct search in this 3D discretized space. A refinement of the rotation estimate can be obtained from the conservation of harmonic coefficients in the rotational shift theorem. A novel decoupling of the shift theorem with respect to the Euler angles is presented and exploited in an iterative scheme to refine the initial rotation estimates. Experiments show the suitability of the method for large rotations and the dependence of the method on bandwidth and the choice of the spherical harmonic coefficients

Accurately scaled 3-D scene reconstruction using a moving monocular camera and a single-point depth sensor

Abstract: A 3-D reconstruction produced using only a single camera and Structure from Motion (SfM) is always up to scale i.e. without real world dimensions. Real-world dimensions are necessary for many applications that require 3-D reconstruction since decisions are made based on the accuracy of the reconstruction and the estimated camera poses. Current solutions to the absence of scale require prior knowledge of or access to the imaged environment in order to provide absolute scale to a reconstruction. It is often necessary to obtain a 3-D reconstruction of an inaccessible or unknown enviroment. This research proposes the use of a basic SfM pipeline for 3-D reconstruction with a single camera while augmenting the camera with a depth measurement for each image by way of a laser point marker. The marker is identified in the image and projected such that its location is determined as the point with highest point density along the projection in the up to scale reconstruction. The known distance to this point provides a scale factor that can be applied to the up to scale reconstruction. The results obtained show that the proposed augmentation does provide better scale accuracy. The SfM pipeline has room for improvement especially in terms of two-view geometry and structure estimations. A proof of concept is achieved that may open the door to improved algorithms for more demanding applications.M.Ing. (Electrical and Electronic Engineering