Van Herk has shown that the erosion/dilation operator with a linear structuring element of an arbitrary length can be implemented in only 3 min/max operations per pixel. In this paper, the algorithm is generalized to erosions and dilations along discrete lines at arbitrary angles. We also address the padding problem; so that the operation can be performed in place without copying the pixels to and from an intermediate buffer. Applications to image filtering and to radial decompositions of discs are presented. Keywords. Mathematical morphology, image filtering, algorithms, recursivity, line and periodic structuring elements, radial decompositions. Name and address of corresponding author: Dr. Pierre Soille LGI2P Ecole des Mines d'Al`es Parc scientifique Georges Besse F--30000 Nimes France Ph.: int+33- 66 38 70 22 Fax: int+33- 66 38 70 74 Email: soille@eerie.fr Pierre Soille is with the Laboratoire de G'enie Informatique et d'Ing'enierie de Production of the Ecole des Mines d'Al`es, Parc...

Abstract In this paper, we propose a simple but effective image prior- dark channel prior to remove haze from a single input image. The dark channel prior is a kind of statistics of the haze-free outdoor images. It is based on a key observation- most local patches in haze-free outdoor images contain some pixels which have very low intensities in at least one color channel. Using this prior with the haze imaging model, we can directly estimate the thickness of the haze and recover a high quality haze-free image. Results on a variety of outdoor haze images demonstrate the power of the proposed prior. Moreover, a high quality depth map can also be obtained as a by-product of haze removal. 1.

Abstract—We propose an efficient and deterministic algorithm for computing the one-dimensional dilation and erosion (max and min) sliding window filters. For a p-element sliding window, our algorithm computes the 1D filter using 1:5 þ oð1Þ comparisons per sample point. Our algorithm constitutes a deterministic improvement over the best previously known such algorithm, independently developed by van Herk [25] and by Gil and Werman [12] (the HGW algorithm). Also, the results presented in this paper constitute an improvement over the Gevorkian et al. [9] (GAA) variant of the HGW algorithm. The improvement over the GAA variant is also in the computation model. The GAA algorithm makes the assumption that the input is independently and identically distributed (the i.i.d. assumption), whereas our main result is deterministic. We also deal with the problem of computing the dilation and erosion filters simultaneously, as required, e.g., for computing the unbiased morphological edge. In the case of i.i.d. inputs, we show that this simultaneous computation can be done more efficiently then separately computing each. We then turn to the opening filter, defined as the application of the min filter to the max filter and give an efficient algorithm for its computation. Specifically, this algorithm is only slightly slower than the computation of just the max filter. The improved algorithms are readily generalized to two dimensions (for a rectangular window), as well as to any higher finite dimension (for a hyperbox window), with the number of comparisons per window remaining constant. For the sake of concreteness, we also make a few comments on implementation considerations in a contemporary programming language. Index Terms—Mathematical morphology, running maximum filter, min-max filter, computational efficiency. æ 1

We propose a novel energy minimisation framework for the dense reconstruction of stereo image sequences that incorporates data fidelity as well as spatial and temporal regularity. An iterated dynamic programming scheme is proposed to minimise the energy function. We also present an efficient implementation of the minimisation scheme by introducing morphological decomposition techniques to solve the dynamic programming subproblem. Our proposed method is capable of reconstructing dynamic scenes with complex motion. Results are presented demonstrating the strength of our proposed algorithm. 1

Several libraries dedicated to mathematical morphology exist. But they lack genericity, that is to say, the ability for operators to accept input of di#erent natures ---2D binary images, graphs enclosing floating values, etc. We describe solutions which are integrated in Olena, a library providing morphological operators. We demonstrate with some examples that translating mathematical formulas and algorithms into source code is made easy and safe with Olena. Moreover, experimental results show that no extra costs at run-time are induced.

We propose a concise definition of the skew angle of document, based on mathematical morphology. This definition has the advantages to be applicable both for binary and grey-scale images. We then discuss various possible implementations of this definition, and show that results we obtain are comparable to those of other existing algorithms.

Abstract—An efficient algorithm is presented for the computation of grayscale morphological operations with arbitrary 2-D flat structuring elements (S.E.). The required computing time is independent of the image content and of the number of gray levels used. It always outperforms the only existing comparable method, which was proposed in the work by Van Droogenbroeck and Talbot, by a factor between 3.5 and 35.1, depending on the image type and shape of S.E. So far, filtering using multiple S.E.s is always done by performing the operator for each size and shape of the S.E. separately. With our method, filtering with multiple S.E.s can be performed by a single operator for a slightly reduced computational cost per size or shape, which makes this method more suitable for use in granulometries, dilation-erosion scale spaces, and template matching using the hit-or-miss transform. The discussion focuses on erosions and dilations, from which other transformations can be derived. Index Terms—Dilation, dilation-erosion scale spaces, erosion, fast algorithm, hit-or-miss transform, mathematical morphology, multiscale analysis. I.

Two new families of algorithms for computing openings of binary and label images are presented in this paper. The first family of algorithms is based on an horizontal scan, and a vertical scan that takes the result of the horizontal scan as input. With the results of these two scans it is possible to compute an opening with respect to a rectangle of any size. The second family of algorithms is based on the construction of an exhaustive list of rectangles included in an object. Rectangles of this list all have a maximal extension, i.e. no larger rectangle included in a region contains them. The opening then results from filling the output image with rectangles larger than the structuring element. After a description of the algorithms we provide a comparison of several algorithms in terms of computation time efficiency. The comparison shows that some of the new algorithms advantageously compete with existing algorithms.

Abstract—Document Image Binarization techniques have been studied for many years, and many practical binarization techniques have been developed and applied successfully on commercial document analysis systems. However, the current state-of-the-art methods, fail to produce good binarization results for many badly degraded document images. In this paper, we propose a self-training learning framework for document image binarization. Based on reported binarization methods, the proposed framework first divides document image pixels into three categories, namely, foreground pixels, background pixels and uncertain pixels. A classifier is then trained by learning from the document image pixels in the foreground and background categories. Finally, the uncertain pixels are classified using the learned pixel classifier. Extensive experiments have been conducted over the dataset that is used in the recent Document Image Binarization Contest(DIBCO) 2009. Experimental results show that our proposed framework significantly improves the performance of reported document image binarization methods. Keywords-document image binarization; image pixel classification; self-training learning framework; I.

Discrete morphologSCV operations with line seg)5 ts are notoriously hard to implement. In this paper we study di#erent possible implementations of the line structuring element, compare them, and examine their rotation and translation invariance in the continuous-domain. That is, we are interested in obtaining a morpholog55fi operator that is invariant to rotations and translations of the im ag before sampling 1