This paper presents a method for dense optical flow estimation in which the motion field within patches that result from an initial intensity segmentation is parametrized with models of different order. We propose a novel formulation which introduces regularization constraints between the model parameters of neighboring patches. In this way, we provide the additional constraints for very small patches and for patches whose intensity variation cannot sufficiently constrain the estimation of their motion parameters. In order to preserve motion discontinuities, we use robust functions as a regularization mean. We adopt a three-frame approach and control the balance between the backward and forward constraints by a real-valued direction field on which regularization constraints are applied. An iterative deterministic relaxation method is employed in order to solve the corresponding optimization problem. Experimental results show that the proposed method deals successfully with motions large in magnitude, motion discontinuities, and produces accurate piecewise-smooth motion fields.

The goal of this paper is to establish the fundamental requirements of any morphological software in such a way as to produce reliable, precise, and generic algorithm representations in order to overcome the combinatorial explosion of the code needed to deal with all possible kinds of data structures and image types. Algorithms should be built with the guarantee that the desired implementation is written once, process data in an abstract way, and is efficient at the same time. Requirements are derived from a review of some of the most used software packages and image libraries with respect to mathematical morphology including [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Such a review makes it possible to characterize their advantages and drawbacks. These aspects call for software for mathematical morphology that has to be generic and should support a large variety of data types.

The watershed algorithm from mathematical morphology is powerful for segmentation. However, it does not allow incorporation of a priori information as segmentation methods that are based on energy minimization. In particular, there is no control of the smoothness of the segmentation result. In this paper, we show how to represent watershed segmentation as an energy minimization problem using the distance-based definition of the watershed line. A priori considerations about smoothness can then be imposed by adding the contour length to the energy function. This leads to a new segmentation method called watersnakes, integrating the strengths of watershed segmentation and energy based segmentation. Experimental results show that, when the original watershed segmentation has noisy boundaries or wrong limbs attached to the object of interest, the proposed method overcomes those drawbacks and yields a better segmentation.

We propose a new method for contour tracking in video. The inverted distance transform of the edge map is used as an edge indicator function for contour detection. Using the concept of topographical distance, the watershed segmentation can be formulated as a minimization. This new viewpoint gives a way to combine the results of the watershed algorithm on different surfaces. In particular, our algorithm determines the contour as a combination of the current edge map and the contour, predicted from the tracking result in the previous frame. We also show that the problem of background clutter can be relaxed by taking the object motion into account. The compensation with object motion allows to detect and remove spurious edges in background. The experimental results confirm the expected advantages of the proposed method over the existing approaches.

Linear filters have two major drawbacks. First, edges in the image are smoothed with increasing filter size. Second, by extending the filters to multi-channel data, correlation between the channels is lost. Only a few researchers have explored the possibilities of mode filtering to overcome these problems. Mode filtering is motivated from both a local histogram with tonal scale and a robust statistics point of view. The tonal scale is proved to be equal to the scale of the error norm function within the robust statistics framework. Instead of the more commonly studied global mode, our focus is on the local mode. It preserves edges and details and is easily extensible to multi-channel data. A generalization of the spatial Gaussian filtering to a spatial and tonal Gaussian filter is used to iterate to the local mode. Results on color images include successful noise attenuation while preserving edges and detail by local mode filtering.

This paper presents the measurement of colored object reflectance, under different, general assumptions regarding the imaging conditions. We exploit the Gaussian scale-space paradigm for color images to define a framework for the robust measurement of object reflectance from color images. Object reflectance is derived from a physical reflectance model based on the Kubelka-Munk theory for colorant layers. Illumination and geometrical invariant properties are derived from the reflectance model. Invariance and discriminative power of the color invariants is experimentally investigated, showing the invariants to be successful in discounting shadow, illumination, highlights, and noise. Extensive experiments show the different invariants to be highly discriminative, while maintaining invariance properties. The presented framework for color measurement is well-founded in the physics of color as well as in measurement science. Hence, the proposed invariants are considered more adequate for the measurement of invariant color features than existing methods.

This paper presents the measurement of object reflectance from color images. We exploit the Gaussian scale-space paradigm to define framework for the robust measurement of object reflectance from color images. Illumination and geometrical invariant properties are derived from a physical reflectance model based on the Kubelka-Munk theory. Imaging conditions are assumed to be white illumination and matte, dull object or general object, respectively. Invariance is denoted by +, whereas sensitivity to the imaging condition is indicated by -. Invariance, discriminative power and localization accuracy of the color invariants is extensively investigated, showing the invariants to be successful in discounting shadow, illumination intensity, highlights, and noise. Experiments show the different invariants to be highly discriminative while maintaining invariance properties. The presented framework for color measurement is well-founded in physics as well as measurement science. The framework is thoroughly evaluated experimentally. Hence is considered more adequate than existing methods for the measurement of invariant color features.

We present a directional boundary representation which deals locally and consistently with the boundary's "inside". We show that collision and wave propagation are reduced to addition on the spectrum of directions, and we derive transformation laws for differential geometrical properties such as directed curvature.

A highly time-consuming activity in many areas of commerce and business is the manual entry into computer of data handwritten on forms. All forms in widespread use contain discrete fields where specific information can be entered. Automatic recognition of these forms could be achieved using existing state-of-the-art OCR algorithms for numerals, alphabetic characters, cursive words, signatures and mark sensing if they could be rapidly configured along with any inter-relationships and dependencies for different forms. This paper describes an initial implementation of an interactive graphical tool to allow the handwritten fields of a form and their inter-relationships to be described and defined for automatic linking with appropriate OCR algorithms. Results indicate that the main requirement is for the operator to have a full understanding of the handwritten form and an ability to describe its contents.

We introduce a class of nonlinear differential equations that are solved using morphological operations. The erosion and dilation act as morphological propagators propagating the initial condition into the "scale-space", much like the Gaussian convolution is the propagator for the linear diffusion equation. The analysis starts in the set domain, resulting in the description of erosions and dilations in terms of contour propagation. We show that the structuring elements to be used must have the property that at each point of the contour there is a well-defined and unique normal vector. Then given the normal at a point of the dilated contour we can find the corresponding point (point-of-contact) on the original contour. In some situations we can even link the normal of the dilated contour with the normal in the point-of-contact of the original contour. The results of the set domain are then generalized to grey value images. The role of the normal is replaced with the function gradient. The same analysis also holds for the erosion. Using a family of increasingly larger structuring functions we are then able to link infinitesimal changes in grey value with the gradient in the image.>

The authors investigate the use of mathematical morphology to construct scale-spaces. These scale-spaces are based on differential equations, which are solved by morphological operators, describing the evolution of images in scale-space.>