In this paper, we propose the application of principal component analysis (PCA) to scale-spaces. PCA is a standard method used in computer vision. Because the translation of an input image into scale-space is a continuous operation, it requires the extension of conventional finite matrix-based PCA to an infinite number of dimensions. Here, we use spectral theory to resolve this infinite eigenvalue problem through the use of integration, and we propose an approximate solution based on polynomial equations. In order to clarify its eigensolutions, we apply spectral decomposition to Gaussian scale-space and scale-normalized Laplacian of Gaussian (sLoG) space. As an application of this proposed method, we introduce a method for generating Gaussian blur images and sLoG images, demonstrating that the accuracy of such an image can be made very high by using an arbitrary scale calculated through simple linear combination. Furthermore, to make the scale-space filtering efficient, we approximate the basis filter set using Gaussian lobes approximation and we can obtain XY-Separable filters. As a more practical example, we propose a new Scale Invariant Feature Transform (SIFT) detector.

In this paper a hardware-efficient local extrema detection (LED) method used for scale-space extrema detection in the SIFT algorithm is proposed. By reformulating the reuse of the intermediate results in taking the local maximum and minimum, the necessary operations in LED are reduced without degrading the detection accuracy. The proposed method requires 25% to 35% less logic resources than the conventional method when implemented in an FPGA with a slight increase in latency.

In this paper, we present a novel framework for analyzing and segmenting point-sampled 3D objects. Our algorithm computes a decomposition of a given point set surface into meaningful components, which are delimited by line features and deep concavities. Central to our method is the extension of the scale-space theory to the three-dimensional space to allow feature analysis and classification at different scales. Then, a new surface classifier is computed and used in an anisotropic diffusion process via partial differential equations (PDEs). The algorithm avoids the misclassifications due to fuzzy and incomplete line features. Our algorithm operates directly on points requiring no vertex connectivity information. We demonstrate and discuss its performance on a collection of point sampled 3D objects including CAD and natural models. Applications include 3D shape matching and retrieval, surface reconstruction and feature preserving simplification.

In this paper, we introduce a new technology to extract the unique features from an iris image, which uses scale-space filtering. Resulting iris code can be used to develop a system for rapid and automatic human identification with high reliability and confidence levels. First, an iris part is separated from the whole image and the radius and center of the iris are evaluated. Next, the regions that have a high possibility of being noise are discriminated and the features presented in the highly detailed pattern are then extracted. In order to conserve the original signal while minimizing the effect of noise, scale-space filtering is applied. Experiments are performed using a set of 272 iris images taken from 18 persons. Test results show that the iris feature patterns of different persons are clearly discriminated from those of the same person.

We describe a multiresolution 3D active balloon model to trace the boundaries of moving object. This model is able to analyze a shape hierarchically using 3D scale-space. The 3D scale-space can be determined by changing the parameters of the active balloon. We extended 2D process-grammar to describe the deformation process between a shape and a sphere, based on topological scale-space analysis. The geometric invariant features were used to analyze the deformation of nonrigid shapes. We analyzed the motion of a heart by using MRI data.

One of the most basic characteristics of the image is accompanied by its blur. It was 1962 that I had discovered for the first time in the world that the blur was a Gaussian type. In this paper the outline is described about historical details concerning this circumstances.

In the image recognition problem, it is very important how we represent the image. Considering this, we propose a new representational method of images based on the stability in scale-space. In our method, the image is segmented and represented as a hierarchical region graph in scale-space. The object is represented as feature graph, which is subgraph of region graph. In detail, the region graph is defined on the image with the relation of each segment hierarchically. And the feature graph is determined based on the "life-time" of the graph of the object in scale-space. This "life-time" means how long feature graph lives when the scale parameter is increased. We apply our method to the face detection problem, which is foundmental and difficult problem in face recognition. We determine the feature graph of the frontal human face statistical point of view. We also build the face detection system using this feature graph to show how our method works efficiently.

A content-based image retrieval scheme based on scale-space theory is proposed. Instead of considering all scales for image retrieval, the proposed algorithm utilizes a modified histogram intersection method to compute the relative scale between a query image and a candidate image. The proposed method has been applied to various images and the performance improvement has been verified.