Grassfire transform

Abstract: An improved apparatus and method for creating high quality virtual reality panoramas is disclosed that yields dramatic improvements during the authoring and projecting cycles, with speeds up to several orders of magnitude faster than prior systems. In a preferred embodiment, a series of rectilinear images taken from a plurality of rows are pairwise registered with one another, and locally optimized using a pairwise objective function (local error function) that minimizes certain parameters in a projective transformation, using an improved iterative procedure. The local error function values for the pairwise registrations are then saved and used to construct a quadratic surface to approximate a global optimization function (global error function). The chain rule is used to avoid the direct evaluation of the global objective function, saving computation. In one embodiment concerning the blending aspect of the present invention, an improved procedure is described that relies on Laplacian and Gaussian pyramids, using a blend mask whose boundaries are determined by the grassfire transform. An improved iterative procedure is disclosed for the blending that also determines at what level of the pyramid to perform blending, and results in low frequency image components being blended over a wider region and high frequency components being blended over a narrower region. Human interaction and input is also provided to allow manual projective registration, initial calibration and feedback in the selection of photos and convergence of the system.

Abstract: This paper presents a system for creating a full 360-degree panorama from rectilinear images captured from a single nodal position. The solution to the problem is divided into three steps. The first step registers all overlapping images projectively. A combination of a gradient-based optimization method and a correlation-based linear search is found to be robust even in cases of drastic exposure differences and small amount of parallax. The second step takes the projective matrices and their associated hessian matrices as inputs, and calibrates the internal and external parameters of every image through a global optimization. The objective is to minimize the overall image discrepancies in all overlap regions while converting projective matrices into camera parameters such as focal length, aspect ratio, image center, 3D orientation, etc. The third step re-projects all images onto a panorama by a Laplacian-pyramid-based blending. The purpose of blending is to provide a smooth transition between images and eliminate small residues of misalignments resulting from parallax or imperfect pairwise registrations. The blending masks are generated automatically through the grassfire transform. At the end, we briefly explain the necessary human interface for initialization, feedback and manual options.

Abstract: The medial axis is an important shape descriptor first introduced by Blum (1967)?1] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a "center point", is needed in various applications ranging from shape alignment to geography. In this paper, we present a uniform approach to define a global shape measure (called extended distance function, or EDF) along the 2D medial axis as well as the center of a 2D shape (called extended medial axis, or EMA). We reveal a number of properties of the EDF and EMA that resemble those of the boundary distance function and the medial axis, and show that EDF and EMA can be generated using a fire propagation process similar to Blum's grassfire analogy, which we call the extended grassfire transform. The EDF and EMA are demonstrated on many 2D examples, and are related to and compared with existing formulations. Finally, we demonstrate the utility of EDF and EMA in pruning medial axes, aligning shapes, and shape description.

Abstract: The principles of SKIPSM (Separated-Kernel Image Processing using Finite State Machines), a powerful new way to implement many standard image processing operations, are presented here and in a group of companion papers. This paper describes the application of SKIPSM to the computation of the Grassfire Transform (GT), the mapping of a binary image into a grey-level image in such a way that the output grey level of each interior pixel of each individual blob is proportional to the distance of that pixel from the blob boundary. Distance can be defined in terms of various norms: Euclidean distance, elliptical distance, 'boxcar' distance, etc. While potentially very useful, the GT has seen limited application because of the many computational steps required to calculate it. In comparison with conventional hardware-based and software-based approaches, SKIPSM allows implementation of the GT at higher speeds and/or lower hardware cost. The key developments upon which this improved performance is based are (1) the separation of 2D the binary erosions on which the GT is based into row operations followed by column operations, (2) the formulation of these row and column operations in a form compatible with pipelined operation, (3) the implementation of the resulting operations as simple finite-state machines, (4) the automated generation of the finite-state machine configuration data for structuring elements (SEs), and (5) the simultaneous application of all these nested SEs in a single pipeline pass. Some key features of SKIPSM, as applied to the GT, are listed below: (1) Because the SEs can be large and arbitrary, any distance measure can be used. There is no penalty involved in using true circles or ellipses, rather that the octagons or squares resulting from sequential application of 3 X 3 SEs. (2) The simultaneous application of six circular erosion stages (SEs of size 3 X 3, 5 X 5, ..., 13 X 13) has already been demonstrated. Eight or more simultaneous circular erosion stages may be possible (sizes 3 X 3, 5 X 5, ..., 17 X 17, ...). (3) The user specifies the SE or SEs. All other steps are automated. These results are can be achieved using conventional pipelined hardware in this new way. Alternatively, inexpensive off-the-shelf 'chips' can be configured to carry out the same operations as conventional image processing hardware. Corresponding 'speedups' are achieved in software-based implementations.2347© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.