We propose a new complex wavelet, the RI-spline wavelet, which is constructed using spline wavelets for dual-tree DWT. In the RI-spline wavelet, the real and imaginary components become an approximate Hilbert pair to each other. Then we propose a new dual-tree algorithm which uses an interpolation method for providing a half-sample-delay between the two filters of the trees. Finally, we experimentally show that the translation invariance, which can not be obtained by the ordinary DWT, is obtained by RI-spline wavelet.

We propose a visual inspection method of defect detection on textile surfaces; selectively removing the textural information from textile surfaces. For this purpose we use wavelet shrinkage, which was originally proposed by Donoho and Johnstone as a method to remove Gaussian white noise (1994, 1995). We also propose a modification of wavelet shrinkage to selectively remove textural information as noise. Once the textural information, is removed from textile surfaces, the remaining inspection processes can be conducted in the image domain. In this way, we can utilize the image processing methods and techniques developed so far for the visual inspection of other industrial products.

We present a method for estimating vanishing points of the object planes using the continuous change of visual spatial frequencies of textures on them. Considering that treating 3D textures in real images is a tough problem, we restrict our problem so that at first, human users point out the rough center of the 3D textured region on a planar surface, and its tilt angle has already been estimated. We show that by adequately choosing the direction, of spatial frequency estimation, the change of visual spatial frequencies of textures on planar surfaces is expressed as an analytic curve which has only two parameters. In order to estimate these parameters, which leads to estimating vanishing points, we adopt a voting strategy similar to the Hough transform. Experimental results show that the proposed method can estimate vanishing points well even in real images.

This paper analyzes photometric properties of occluding edges and proves that an object surface behind a nearer object is partially observable beyond the occluding edges. We first discuss a limitation of the image blurring model using the convolution, and then present an optical flux based blurring model named the reversed projection blurring (RPB) model. Unlike the multicomponent blurring model proposed by Nguyen et al., the RPB model enables us to explore the optical phenomena caused by a shift-variant point spread function that appears at a depth discontinuity. Using the RPB model, theoretical analysis of occluding edge properties are given and two characteristic phenomena are shown: (1) a blurred occluding edge produces the same brightness profiles as would be predicted for a surface edge on the occluding object when the occluded surface radiance is uniform and (2) a nonmonotonic brightness transition would be observed in blurred occluding edge profiles when the occluded object has a surface edge. Experimental results using real images have demonstrated the validity of the RPB model as well as the observability of the characteristic phenomena of blurred occluding edges.

A focus-based passive range sensor is presented. As a basic principle this range sensor uses Asada et al's method (1993), which models the blurring of an ideal linear step edge and calculates edge depth by fitting this model to multi-focus images. However the applicability of their method to a real scene is open, because the assumption of an ideal linear step edge is not always true, especially in real scenes. In order to deal with this problem, we first detect a resolution level focused edge position without any specific model. Then using the fact that edge point intensity is focal invariant, we adaptively select the proper focal scope within which the linear step edge model can be applied by changing a focus parameter sequentially around a resolution level focused edge position. The experiments show that the prototype range sensor can estimate depth of a general edge including centers at a distance of 2.5 m with 0.43% accuracy.

This paper analyzes photometric properties of occluding edges and proves that (1) we can observe surface edges on the farther object located close to the occluding edge even if they are occluded by the nearer object, (2) the image of an occluding edge coincides with that of a surface edge on the nearer object if the brightness of the farther object is uniform around the occluding edge. First, we propose a blurring model named the reversed projection blurring model to analyze photometric properties of blurring phenomena of an occluding edge. Using this model, the theoretical proof of the two properties mentioned above is given. Finally, experimental results in real world environments demonstrate the validity of our blurring model as well as the observability of the photometric properties of occluding edges.>