In this study, we introduce a software pipeline to track feature points across endoscopic video frames. It deals with the common problems of low contrast and uneven illumination that afflict endoscopic imaging. In particular, irregular feature trajectories are eliminated to improve quality. The structure of soft tissue is determined by an iterative factorization method based on collection of tracked features. A shape updating mechanism is proposed in order to yield scale-invariant structures. Experimental results show that the tracking method produced good tracking performance and increased the number of tracked feature trajectories. The real scale and structure of the target scene was successfully estimated, and the recovered structure is more accuracy than the conventional method.

We propose a method for the recovery of projective structure and motion by the factorization of the rank 1 matrix containing the images of all points in all views. In our method, the unknowns are the 3D motion and relative depths of the set of points, not their 3D positions. The coordinates of the points along the camera plane are given by their image positions in the first frame. The knowledge of the coordinates along the camera plane enables us to solve the SFM problem by iteratively factorizing the rank 1 matrix. This simplifies the decomposition compared with the SVD (Singular Value Decomposition). Experiments with both simulated and real data show that the method is efficient for the recovery of projective structure and motion.

The reconstruction of motion and structure from multiple images is fundamental and important problem in computer vision. This paper highlights the recovery of the camera motion and the object shape under some camera projection model from feature correspondences especially the epipolar geometry and the factorization method for mainly used projection models.

This paper describes a factorization-based algorithm that reconstructs 3D object structure as well as motion from a set of multiple uncalibrated perspective images. The factorization method introduced by Tomasi-Kanade is believed to be applicable under the assumption of linear approximations of imaging system. In this paper we describe that the method can be extended to the case of truly perspective images if projective depths are recovered. We established this fact by interpreting their purely mathematical theory in terms of the projective geometry of the imaging system and thereby, giving physical meanings to the parameters involved. We also provide a method to recover them using the fundamental matrices and epipoles estimated from pairs of images in the image set. Our method is applicable for general cases where the images are not taken by a single moving camera but by different cameras having individual camera parameters. The experimental results clearly demonstrates the feasibility of the proposed method.

A new application of the factorization method is reported for 3-D shape reconstruction from endoscope image sequences. The feasibility of the method is verified with some theoretical considerations and results of extensive experiments. This method was developed by Tomasi and Kanade, and improved by Poelman and Kanade, with the aim of achieving accurate shape reconstruction by using a large number of points and images, and robustly applying well-understood matrix computations. However, the latter stage of the method, called normalization, is not as easily understandable as the use of singular value decomposition in the first stage. In fact, as shown in this report, many choices are possible for this normalization and a variety of results have been obtained depending on the choice. This method is easy to understand, easy to implement, and provides sufficient accuracy when the approximation used for the optical system is reasonable. However, the details of the theoretical basis require further study.

This paper discusses the fixed-point smoothing and filtering problems given lumped covariance function of a scalar signal process observed with additive white Gaussian noise. The recursive Wiener smoother and filter are derived by applying an invariant imbedding method to the Volterra-type integral equation of the second kind in linear least-squares estimation problems. The resultant estimators in Theorem 2 require the information of the crossvariance function of the state variable with the observed value, the system matrix, the observation vector, the variance of the observation noise and the observed value. Here, it is assumed that the signal process is generated by the state-space model. The spectral factorization problem is also considered in Sects. 1 and 2.