A Hillclimbing Approach to Image Mosaics

This paper presents a hillclimbing approach to image mosaic creation. Our approach significantly differs from previous approaches by being non-deterministic and allowing for tile overlapping, which produces a collage effect. Results show that, if refined, the hillclimbing approach to mosaic creation may have the potential to provide a viable alternative to other techniques. INTRODUCTION Mosaics are images that are created by arranging many smaller components, called tiles, on a canvas. This art form has been around since ancient times and has taken a variety of forms over the years. Recently, many have researched ways to automate the creation of mosaics through the use of computers. The Simulated Decorative Mosaic [Hausner, 2001] algorithm generates mosaics that are composed of many small, uniformly colored tiles. Photomosaics [Silvers and Hawley, 1997] are created by placing rectangular tile images in a contiguous fashion on a canvas such that they resemble the original picture at far distances. Most important to our project, the Jigsaw Image Mosaic [Kim and Pellacini, 2002] generates mosaics from many smaller tile images, which are placed at arbitrary points, rotated by an arbitrary angle, and deformed in non-uniform but visually appealing ways. In this paper, we introduce a new approach to image mosaics that uses an optimization heuristic in the form of a hillclimbing algorithm. Like the Jigsaw Image Mosaic, our mosaics are created from arbitrarily shaped tile images that are transformed to fill objects within a target scene. This approach deviates from previous work in two ways: first, it relies on a random initialization step, thereby rendering the creation of image mosaics a non-deterministic process and second, we allow tiles to overlap, which creates a collage effect in the output image. FORMAL PROBLEM STATEMENT The problem we set out to solve can be stated thus: Given a target image and a set of arbitrarily shaped image tiles, find an optimal arrangement of N tiles such that they resemble the target picture as closely as possible. Tiles in this instance can be placed anywhere on the canvas, and can be rotated or scaled by arbitrary values. Formally, we define a four dimensional vector A as an arrangement for tile i in the set of N: An output image can then be constructed from the arrangement vector, A, by sequentially painting each tile on an initially empty canvas using the specified translation, rotation and scaling parameters. (Note that order of tile placement is significant in this definition since tiles that occur early in the arrangement may be obscured by tiles that occur later in the arrangement.) For the purpose of this paper, we define a function I that renders an arrangement vector, creating a mosaic: In order to evaluate the quality of a given tile arrangement A, a function, Diff(Target, I(A)), is defined that gives the difference between the target image and I(A). The problem is then to search for a tile arrangement A such that ♥ It should be noted that within the context of this paper tile will refer to an arbitrarily shaped image.