Ibrahim Gokcen

Binary image transformation using two-dimensional chaotic maps

We present an algorithm for binary image transformation using chaotic maps. Because of its random-like behavior, chaos is a good candidate for encryption. We show that a two-dimensional discrete time dynamical system with one positive Lyapunov exponent allows the transformation of the image in an unpredictable manner. The suggested algorithm acts on the pixel position, where the diffusion property resulting from the sensitivity to the initial states is used to accomplish the transformation in a random-like way. The suggested algorithm uses three types of keys: initial state, external parameters and the number of iterations. Using the so-called Henon map as an example, we show that the algorithm produces almost uncorrelated images even when the keys are slightly changed, making it an attractive and fast method for image encryption.

Comparing Linear Discriminant Analysis and Support Vector Machines

Both Linear Discriminant Analysis and Support Vector Machines compute hyperplanes that are optimal with respect to their individual objectives. However, there can be vast differences in performance between the two techniques depending on the extent to which their respective assumptions agree with problems at hand. In this paper we compare the two techniques analytically and experimentally using a number of data sets. For analytical comparison purposes, a unified representation is developed and a metric of optimality is proposed.

Chaotic gray-level image transformation

We deal with the applications of a class of nonlinear dynamic systems to image transformation and encoding whereby the nonlinear system presents a chaotic or hyperchaotic attractor. Several ways are possible to encode or transform the image using chaos. We develop algorithms for image encoding based on the permutation of the pixel value, position, or both. This approach enables the fast decorrelation of relations among pixels in the initial image in a random-like fashion. We illustrate the use of 1-D, 2-D, and 3-D maps for this purpose. We also use chaotic dynamical systems with a single or two outputs. A discussion of the sensitivity of the algorithms to the keys is followed by the illustration of the algorithms using example images.

Image Feature Set for Correspondence Mappings

We present a method to automatically construct features capable of putting images in correspondence with each other (i.e., registration) without requiring control points or landmarks on the images in question. Our method is based primarily on Principal Component Analysis (PCA) and a suitable image representation. The feature set is a collection of weight vectors and the correspondence mapping is done using the distances between those vectors. Only a small number of vectors is needed. While we illustrate the approach in the context of image registration, other applications of this method are possible, like distributed sensor networks, specifically when a sensor network is built up from observing devices, like camcorders, CCDs, etc. Most notably, the method could be used for image matching and retrieval, being insensitive to rotation.

Fuzzy Content-Based Retrieval in Image Databases

Image data is a very commonly used multimedia data type and usually have visual characteristics that have imprecise descriptions. Fuzzy retrieval of images that are stored in an image database is a natural and effective way to access image data. Recently, some work has been done on fuzzy content-based retrieval systems but to the authors knowledge none of them rely on a defined model for fuzzy query processing part. In this paper, an approach for fuzzy content-based retrieval using the Fuzzy Object-Oriented Data (FOOD) model will be described. A novel way of determining the fuzzy values from extracted color features will also be presented.

Comparing optimal bounding ellipsoid and support vector machine active learning

In this paper we propose two active learning algorithms combining statistical active learning methods based on SVM and optimal bounding algorithms (OBE) of adaptive system identification. We unify SVM and OBE by demonstrating the similarities and representing SVM in the OBE interpretation. Samples are judiciously selected based on a volume measure provided by OBE using both simple heuristic and greedy optimal strategies. Preliminary experiments illustrate the effectiveness of the proposed algorithms as compared to similar methods.

Adaptive image registration for remote sensing

Remote sensing applications require image registration as a pre-processing step before further progress. In this paper, we present a rigid search-space reducing, feature-based adaptive image registration scheme to put images in correspondence, without establishing explicit point correspondences. Our method estimates the registration parameters using a feature set, which is based on Principal Component Analysis (PCA). A unique aspect of the method is the incorporation of a learning process to learn the parameters from a training set of images, which is constructed incrementally. We illustrate the robustness of this approach using a number of remote sensing images and a variety of rotation angles. Mapping between the features and the transformation parameters is via a nearest-mean matching scheme. Hence correct orientation is determined within a predetermined error.