Kenji Shoji

Assembly of puzzles using a genetic algorithm

In this paper, we proposed a method for solving the rectangle piece jigsaw puzzle assembly problem. A shape of a piece is a rectangle, and a picture of a puzzle is only painted in black and white, i.e., puzzles are processed as binary images. The assembly of the puzzle is performed only using information of the pixel value on the border line of the pieces. This problem cannot be solved by the simple local piece matching because there are many similar pieces. Global matching is required. The proposed method utilizes a genetic algorithm (GA) to search the optimum piece arrangement because GA has the ability to find the global solution in the large optimization space. The proposed method correctly assembled all pieces in the 8 /spl times/ 8-piece puzzle.

3-D interpretation of single line drawings based on entropy minimization principle

The human visual system can interpret two-dimensional (2-D) line drawings like the Necker cube as three-dimensional (3-D) wire frames. On this human ability Thomas Marill presented two important papers. First one proposed the 3-D interpretation model based on the principle to minimize the standard deviation of the angles between line segments in 3-D wire frame (MSDA), and reported the results of simulation experiments. Second one proposed the principle to minimize the description length on the internal representation in visual system. Motivated by Marills principle to minimize the description length, we propose a principle to minimize the entropy of angle distribution between line segments in a 3-D wire frame (MEAD), which is more general than the MSDA one. And we implement the principle MEAD using a genetic algorithm (GA) as a simulation program. The results of simulation experiments show that the proposed principle of MEAD is more appropriate than the MSDA and another principle.

Model-based pose estimation using genetic algorithm

In this paper, we propose a method of the model-based pose estimation in the 3D world from a 2D image. This process consists in searching for the best value of coordinates (x, y, z) and of rotating angles (/spl theta//sub x/, /spl theta//sub y/, /spl theta//sub z/) in which the model object matches most exactly the given input edge image. Taking the match of objects as an index on the six-parameter space, this process can be regarded as a maximum searching problem. We use a genetic algorithm in the estimation of those parameters, and propose a new concept of fitness which takes edge direction into consideration. Our experiments show the results of the proposed method on edge input images.

Pose estimation of a 2D articulated object from its silhouette using a GA

This paper proposes a model-based method for estimating the pose of a 2D articulated object from a single silhouette image using a genetic algorithm (GA). In this study, a human body viewed sideways is treated as a 2D articulated object. The model of the articulated object is given as a stick one. Its pose is represented in 2D position of the main stick and angles of all sticks connected at joints. The parameter space for representing the pose of the stick model is very large. Therefore, we limit the search space to the range in which the stick model does not protrude from the silhouette. For the search space limitation, the region of position and angle of the stick perfectly included in the silhouette is obtained for each stick in advance. The pose of the stick model is evaluated in the sum of the proximity measure from each pixel in the silhouette to the stick model. Experiments with synthetic silhouettes by a human figure design tool show that the proposed method can estimate various poses and that it can be applied to several human figures with a single stick model.

Assembly of puzzles by connecting between blocks

In this paper, we proposed a method for solving the rectangle piece jigsaw puzzle assembly problem. A shape of a piece is a rectangle, and a puzzle image is RGB full color. The assembly of the puzzle is performed only using information of the pixel value on the border line of the piece. Pieces are connected by a matching function between two pieces. Not only the best matched piece is connected. The matching values to other pieces are used in the evaluation between two pieces. A simple method of puzzle assembly is that a single piece is connected to a block which is defined as a group of connected pieces. But types of piece combinations are restricted in the simple method. In the proposed method, each block is connected each other. Therefore, the best matched connection is selected from many types of combinations between pieces and blocks. The proposed method correctly assembled all pieces in 16 × 12-piece puzzles.

An iterated greedy algorithm for the node placement problem in bidirectional Manhattan street networks

Wavelength Division Multiplexing (WDM) is a technology which multiplexes optical carrier signals on a single optical fiber by using different wavelengths. Lightwave networks based on WDM are promising ones for high-speed communication. If network nodes are equipped with tunable transmitters and receivers, a logical topology can be changed by reassigning wavelengths to tunable transceivers of nodes. Network performance is influenced by the logical node placements. Therefore, an efficient algorithm to obtain the optimal node placement to achieve the best network performance is necessary. In this paper, an iterated greedy algorithm is proposed for this node placement problem. The proposed iterated greedy algorithm consists of two phases, construction and destruction phases. As a local search algorithm, variable depth search is applied after the construction phase. The computational results showed that this iterated greedy algorithm outperformed the best metaheuristic algorithm for this problem.

An algorithm for affine transformation of binary images stored in pxy tables by run format

The algorithm for an affine transformation (such as magnification, reduction, or rotation of a binary image) using a run format and a combination of a skew transformation and a transposition has been known. A transposition using this conventional algorithm requires a relatively large amount of computation time, although its skewing operation is simple and fast. This paper proposes an efficient method of transposition of an image represented by a run format, and its applications to an affine transformation (e.g., rotation, magnification, and reduction of an image). The proposed method uses a simple run data format “pxy tables,” in which the start coordinate of black and white runs are stored alternatively in a one-dimensional array. An experimental comparison of the proposed method with a conventional method shows that the computation time per run of the former is constant, while that of the latter increases with the length of the black runs. In other words, the computation time of an affine transformation of a binary image by using the proposed method is approximately proportional to the number of runs alone.

Generalized skeleton representation and adaptive rectangular decomposition of binary images

This report presents a technique of decomposing an arbitrary binary image into the union of rectangles so that the number of rectangles becomes as small as possible. This decomposition is referred as adaptive rectangular decomposition. Decomposing a binary image into objects with a same basic shape but with different sizes is familiar as morphological skeleton decomposition. To implement adaptive rectangular decomposition, we generalize the discrete version of morphological skeleton decomposition by replacing a sequences of disks {nB}, n equals 0,1, (DOT)(DOT)(DOT) with a structuring element sequence {Bn}, where Bn equals Bn-1 (direct sum) Gn-1 and Gn is called a generator. A good selection of each generator in a generator sequence {Gn} makes a compact representation of a given binary image. In adaptive rectangular decomposition, we restrict each generator Gn by one of only two objects; the vertical 2-pixel line V and the horizontal 2-pixel line H. The adaptive rectangular decomposition algorithm selects the best sequence {Gn} using dynamic programming (DP) technique. In some experiments, we compared adaptive rectangular decomposition with other types of decomposition in the viewpoint of the time cost of morphological operations by decomposed structuring elements (decomposed binary images). Experimental results show that the time cost of the operations by the structuring elements represented by adaptive rectangular decompositions is smaller than the case of other types of decompositions.

A new fitness function for shape detection using genetic algorithm

When genetic algorithms (GA) are used for shape detection, the fitness function (evaluation function for chromosomes) must be designed in an appropriate way. Considering shape detection in terms of finding the parameters of model objects to provide the best matching with an input edge image, the chromosome is defined in terms of the objects parameters, and the fitness function is defined in terms of the rate of matching between the edge image of a model object generated using the chromosomes parameters and the input edge image. In this study, the model image and input image are divided into four images each by applying four directional filters, and the fitness function is defined as the sum of the matching rates for each edge direction. Experiments with flat objects were performed to compare the proposed fitness with the conventional technique. The results suggested that the proposed method required slightly more computation time (about 10%) than the conventional fitness function while improving the matching rate from 49% to 93%.

Image mosaicing from a set of images without configuration information

We proposed a method for creating image mosaics automatically under the condition that arrangement of partial images or camera movement is unknown. In this problem, the process can be divided into two steps. The first step is to search rough arrangements of partial images. The next step is to adjust detailed positioning using rough arrangements. In the first step, it is difficult to check up all combinations of arrangements because the number of them is huge. The proposed method utilizes a genetic algorithm (GA) for the first step. The second one for detailed positioning is performed by local search.