The fact that objects in the world appear in different ways depending on the scale of observation has important implications if one aims at describing them. It shows that the notion of scale is of utmost importance when processing unknown measurement data by automatic methods. In their seminal works, Witkin (1983) and Koenderink (1984) proposed to approach this problem by representing image structures at different scales in a so-called scale-space representation. Traditional scale-space theory building on this work, however, does not address the problem of how to select local appropriate scales for further analysis. This article proposes a systematic methodology for dealing with this problem. A framework is proposed for generating hypotheses about interesting scale levels in image data, based on a general principle stating that local extrema over scales of different combinations of γ-normalized derivatives are likely candidates to correspond to interesting structures. Specifically, it is shown how this idea can be used as a major mechanism in algorithms for automatic scale selection, which

Leonard McMillan Jr. An Image-Based Approach to Three-Dimensional Computer Graphics (Under the direction of Gary Bishop) The conventional approach to three-dimensional computer graphics produces images from geometric scene descriptions by simulating the interaction of light with matter. My research explores an alternative approach that replaces the geometric scene description with perspective images and replaces the simulation process with data interpolation. I derive an image-warping equation that maps the visible points in a reference image to their correct positions in any desired view. This mapping from reference image to desired image is determined by the center-of-projection and pinhole-camera model of the two images and by a generalized disparity value associated with each point in the reference image. This generalized disparity value, which represents the structure of the scene, can be determined from point correspondences between multiple reference images. The image-warpi...

We present an energy based approach to estimate a dense disparity map between two images while preserving its discontinuities resulting from image boundaries. We first derive a simplied expression for the disparity that allows us to easily estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scale-space. We prove the existence and uniqueness of the underlying parabolic partial differential equation. Experimental results on bot...

Local scale information extracted from visual data in a bottom- up manner constitutes an important cue for a large number of visual tasks. This article presents a framework for how the computation of such scale descriptors can be performed in real time on a standard computer.

This paper outlines a general framework for automatic selection in temporal scale-space representations, and shows how the suggested theory applies to motion detection and motion estimation.

A model for computing image flow in image sequences containing a very wide range of instantaneous flows is proposed. This model integrates the spatio-temporal image derivatives from multiple temporal scales to provide both reliable and accurate instantaneous flow estimates. The integration employs robust regression and automatic scale weighting in a generalized brightness constancy framework. In addition to instantaneous flow estimation the model supports recovery of dense estimates of image acceleration and can be readily combined with parameterized flow and acceleration models. A demonstration of performance on image sequences of typical human actions taken with a high frame-rate camera is given. 1 Introduction Image motion estimation involves relating temporal changes in image intensity across the spatial dimensions. Articulated and deformable motions such as those encountered in images of humans in motion give rise to image sequences having, instantaneously, a wide range of flow m...

Using a Gaussian scale space, one can use the extra dimension, viz. scale, for investigation of "built-in" properties of the image in scale space. We show that one of such induced properties is the nesting of special iso-intensity manifolds, that yield an implicit present hierarchy of the critical points and regions of their influence, in the original image. Its very nature allows one not only to segment the original image automatically, but also to apply "logical filters" to it, obtaining simplified images. We give an algorithm deriving this hierarchy and show its effectiveness on two different kinds of images, both with respect to segmentation and simplification.

In this paper, we focus on the robustness and stability of our algorithm to plot the position of an endoscopic camera (during a colonoscopy procedure) on the corresponding pre-operative CT scan of the patient. The colon has few topological landmarks, in contrast to bronchoscopy images, where a number of registration algorithms have taken advantage of features such as anatomical marks or bifurcations. Our method estimates the camera motion from the optic-flow computed from the information contained in the video stream. Optic-flow computation is notoriously susceptible to errors in estimating the motion field. Our method relies on the following features to counter this, (1) we use a small but reliable set of feature points (sparse optic-flow field) to determine the spatio-temporal scale at which to perform optic-flow computation in each frame of the sequence, (2) the chosen scales are used to compute a more accurate dense optic flow field, which is used to compute qualitative parameters relating to the main motion direction, and (3) the sparse optic-flow field and the main motion parameters are then combined to estimate the camera parameters. A mathematical analysis of our algorithm is presented to illustrate the stability of our method, as well as comparison to existing motion estimation algorithms. We present preliminary results of using this algorithm on both a virtual colonoscopy image sequence, as well as a colon phantom image sequence. 1.

We can supplement the clinical value of an optical colonoscopy procedure if we can continuously co-align corresponding virtual colonoscopy (from preoperative X-ray CT exam) and optical colonoscopy images. In this work, we demonstrate a computer vision algorithm based on optical flow to compute egomotion from live colonoscopy video, which is then used to navigate and visualize the corresponding patient anatomy from X-ray CT data. The key feature of the algorithm lies in the effective combination of sparse and dense optical flow fields to compute the Focus of Expansion(FOE); FOE permits independent computation of camera translational and rotational parameters, directly contributing to the algorithm’s accuracy and robustness. We performed extensive evaluation via a colon phantom and clinical colonoscopy data. We constructed two colon like phantoms, a straight phantom and a curved phantom to measure actual colonoscopy motion; tracking accuracy was quantitatively evaluated by comparing estimated motion parameters(velocity and displacement) to ground truth. Thirty straight and curved phantom sequences were collected at 10, 15 and 20mm/sec(5 trials at each speed), to simulate typical velocities during colonoscopy procedures. The average error in velocity estimation was within 3mm/sec in both straight and curved phantoms. Displacement error was under 7mm over a total distance of 287-288mm in the straight and curved phantoms. Algorithm robustness was successfully demonstrated on 27 optical colonoscopy image sequences from 20 different patients, and spanning 5 different