# Recursive Structure from Motion

19 Dec 2016-pp 109-119

TL;DR: A technique that estimates the Structure from Motion (SFM) in a recursive fashion by recursively performing the SFM on the incoming set of images and updating the previously reconstructed structure with the structure estimated from the current set of photographs.

Abstract: In this paper we present a technique that estimates the Structure from Motion (SFM) in a recursive fashion. Traditionally successful SFM algorithms take the set of images and estimate the scene geometry and camera positions either using incremental algorithms or the global algorithms and do the refinement process [2] to reduce the reprojection error. In this work it is assumed that we don’t have complete image set at the start of the reconstruction process, unlike most of the traditional approaches present in the literature. It is assumed that the set of images come in at the regular intervals and we recursively perform the SFM on the incoming set of images and update the previously reconstructed structure with the structure estimated from the current set of images. The proposed system has been tested on two datasets which consist of 12 images and 60 images respectively and reconstructions obtained show the validity of our proposed technique.

##### References

More filters

••

[...]

TL;DR: This paper presents a method for extracting distinctive invariant features from images that can be used to perform reliable matching between different views of an object or scene and can robustly identify objects among clutter and occlusion while achieving near real-time performance.

Abstract: This paper presents a method for extracting distinctive invariant features from images that can be used to perform reliable matching between different views of an object or scene. The features are invariant to image scale and rotation, and are shown to provide robust matching across a substantial range of affine distortion, change in 3D viewpoint, addition of noise, and change in illumination. The features are highly distinctive, in the sense that a single feature can be correctly matched with high probability against a large database of features from many images. This paper also describes an approach to using these features for object recognition. The recognition proceeds by matching individual features to a database of features from known objects using a fast nearest-neighbor algorithm, followed by a Hough transform to identify clusters belonging to a single object, and finally performing verification through least-squares solution for consistent pose parameters. This approach to recognition can robustly identify objects among clutter and occlusion while achieving near real-time performance.

42,225 citations

••

[...]

TL;DR: New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.

Abstract: A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing

20,503 citations

••

[...]

TL;DR: In this article, the problem of least square problems with non-linear normal equations is solved by an extension of the standard method which insures improvement of the initial solution, which can also be considered an extension to Newton's method.

Abstract: The standard method for solving least squares problems which lead to non-linear normal equations depends upon a reduction of the residuals to linear form by first order Taylor approximations taken about an initial or trial solution for the parameters.2 If the usual least squares procedure, performed with these linear approximations, yields new values for the parameters which are not sufficiently close to the initial values, the neglect of second and higher order terms may invalidate the process, and may actually give rise to a larger value of the sum of the squares of the residuals than that corresponding to the initial solution. This failure of the standard method to improve the initial solution has received some notice in statistical applications of least squares3 and has been encountered rather frequently in connection with certain engineering applications involving the approximate representation of one function by another. The purpose of this article is to show how the problem may be solved by an extension of the standard method which insures improvement of the initial solution.4 The process can also be used for solving non-linear simultaneous equations, in which case it may be considered an extension of Newton's method. Let the function to be approximated be h{x, y, z, • • • ), and let the approximating function be H{oc, y, z, • • ■ ; a, j3, y, ■ • ■ ), where a, /3, 7, • ■ ■ are the unknown parameters. Then the residuals at the points, yit zit • • • ), i = 1, 2, ■ • • , n, are

10,148 citations

••

[...]

TL;DR: A recognition scheme that scales efficiently to a large number of objects and allows a larger and more discriminatory vocabulary to be used efficiently is presented, which it is shown experimentally leads to a dramatic improvement in retrieval quality.

Abstract: A recognition scheme that scales efficiently to a large number of objects is presented. The efficiency and quality is exhibited in a live demonstration that recognizes CD-covers from a database of 40000 images of popular music CDs. The scheme builds upon popular techniques of indexing descriptors extracted from local regions, and is robust to background clutter and occlusion. The local region descriptors are hierarchically quantized in a vocabulary tree. The vocabulary tree allows a larger and more discriminatory vocabulary to be used efficiently, which we show experimentally leads to a dramatic improvement in retrieval quality. The most significant property of the scheme is that the tree directly defines the quantization. The quantization and the indexing are therefore fully integrated, essentially being one and the same. The recognition quality is evaluated through retrieval on a database with ground truth, showing the power of the vocabulary tree approach, going as high as 1 million images.

3,908 citations

##### Related Papers (5)

[...]

[...]

[...]

[...]

[...]