Many problems in document image analysis can be couched in geometric terms. We outline recent advances in computational geometry that contribute to many aspects of the document analysis process and we provide pointers to a selection of the computational geometry literature where the most relevant results can be found. 1 Introduction Document image analysis (DIA) is concerned with the automatic transfer by machine of visual two-dimensional documents, most commonly consisting of printed pages from books, magazines or newspapers. Maps and engineering drawings constitute another class of common documents. The first class of problems have much in common with optical character recognition (OCR) and both with computer vision. On the other hand DIA is a special case of computer vision and therefore its special properties give rise to special sub-problems such as text-block isolation and textline-orientation inference. Furthermore these special properties allow the tailoring of more gener...

For the manufacture of milled parts, it is well known that the size of the cutter significantly affects the machining time. However, for small-batch manufacturing, the time spent on loading tools into the tool magazine and establishing z-length compensation values is just as important. If we can select a set of milling tools that will produce good machining time on more than one type of parts, then several unnecessary machine-tool reconfiguration operations can be eliminated. This paper describes a geometric algorithm for finding an optimal set of cutters for machining a set of 22D parts. In selecting milling cutters we consider both the tool loading time and the machining time and generate solutions that allow us to minimize the total machining time. Our problem formulation addresses the general problem of how to cover a target region to be milled with a cylindrical cutter without intersecting with the obstruction region; this definition allows us to handle both open and closed edges in the target region. Our algorithm improves upon previous work in the tool selection area in following ways: (1) in selecting cutters, it accounts for the tool loading time, and (2) it can simultaneously consider multiple different parts and select the optimal set of cutters to minimize the total manufacturing time.

: In this paper, we describe a new geometric algorithm to determine the biggest feasible cutter size for 2-D milling operations to be performed using a single cutter. In particular: . We give a general definition of the problem as the task of covering a target region without interfering with an obstruction region. This definition encompasses the task of milling a general 2-D profile that includes both open and closed edges. . We discuss three alternative definitions of what it means for a cutter to be feasible, and explain which of these definitions is most appropriate for the above problem. . We present a geometric algorithm for finding the maximal cutter for 2-D milling operations, and we give an outline of a proof that our algorithm is correct. 1 INTRODUCTION NC machining is being used to create increasingly complex shapes. These complex shapes are used in a variety of defense, aerospace, and automotive applications to (1) provide performance improvements, and (2) create high p...

Complexities of applications implemented on embedded and programmable systems grow with the advances in capacities and capabilities of these systems. Mapping applications onto them manually is becoming a very tedious task. This draws attention to using high-level synthesis within design flows. Meanwhile, it is essential to provide a flexible formulation of optimization objectives as well as to perform efficient planning for various design objectives early on in the design flow. In this work, we address these issues in the context of data flow graph (DFG) scheduling which is an essential element within the high-level synthesis flow. We present a algorithm that schedules a chain of operations with data dependencies among consecutive operations at a single step. This local problem is repeated to generate the schedule for the whole DFG. The local problem is formulated as a maximum weight noncrossing bipartite matching. We use a technique from computational geometry domain to solve the matching problem.

This document contains the draft version of the following paper: Z. Yao, S.K. Gupta, and D.S. Nau. A geometric algorithm for finding the largest milling cutter. Journal of Manufacturing Processes, 3(1):1-16, 2001. Readers are encouraged to get the official version from the journal’s web site or by