Convex Structuring Element Decomposition for Single Scan Binary Mathematical Morphology

International audienceThis paper presents a structuring element decomposition method and a corresponding morphological erosion algorithm able to compute the binary erosion of an image using a single regular pass whatever the size of the convex structuring element. Similarly to classical dilation-based methods, the proposed decomposition is iterative and builds a growing set of structuring elements. The novelty consists in using the set union instead of the Minkowski sum as the elementary structuring element construction operator. At each step of the construction, already-built elements can be joined together in any combination of translations and set unions. There is no restrictions on the shape of the structuring element that can be built. Arbitrary shape decompositions can be obtained with existing genetic algorithms with an homogeneous construction method. This paper, however, addresses the problem of convex shape decomposition with a deterministic method

Morphological operations in image processing and analysis

Morphological operations applied in image processing and analysis are becoming increasingly important in today\u27s technology. Morphological operations which are based on set theory, can extract object features by suitable shape (structuring elements). Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure which based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing. In this dissertation, basic morphological operations are reviewed, algorithms and theorems are presented for solving problems in distance transformation, skeletonization, recognition, and nonlinear filtering. A skeletonization algorithm using the maxima-tracking method is introduced to generate a connected skeleton. A modified algorithm is proposed to eliminate non-significant short branches. The back propagation morphology is introduced to reach the roots of morphological filters in only two-scan. The definitions and properties of back propagation morphology are discussed. The two-scan distance transformation is proposed to illustrate the advantage of this new definition. G-spectrum (geometric spectrum) which based upon the cardinality of a set of non-overlapping segments in an image using morphological operations is presented to be a useful tool not only for shape description but also for shape recognition. The G-spectrum is proven to be translation-, rotation-, and scaling-invariant. The shape likeliness based on G-spectrum is defined as a measurement in shape recognition. Experimental results are also illustrated. Soft morphological operations which are found to be less sensitive to additive noise and to small variations are the combinations of order statistic and morphological operations. Soft morphological operations commute with thresholding and obey threshold superposition. This threshold decomposition property allows gray-scale signals to be decomposed into binary signals which can be processed by only logic gates in parallel and then binary results can be combined to produce the equivalent output. Thus the implementation and analysis of function-processing soft morphological operations can be done by focusing only on the case of sets which not only are much easier to deal with because their definitions involve only counting the points instead of sorting numbers, but also allow logic gates implementation and parallel pipelined architecture leading to real-time implementation. In general, soft opening and closing are not idempotent operations, but under some constraints the soft opening and closing can be idempotent and the proof is given. The idempotence property gives us the idea of how to choose the structuring element sets and the value of index such that the soft morphological filters will reach the root signals without iterations. Finally, summary and future research of this dissertation are provided

Image watermarking, steganography, and morphological processing

With the fast development of computer technology, research in the fields of multimedia security, image processing, and robot vision have recently become popular. Image watermarking, steganogrphic system, morphological processing and shortest path planning are important subjects among them. In this dissertation, the fundamental techniques are reviewed first followed by the presentation of novel algorithms and theorems for these three subjects. The research on multimedia security consists of two parts, image watermarking and steganographic system. In image watermarking, several algorithms are developed to achieve different goals as shown below. In order to embed more watermarks and to minimize distortion of watermarked images, a novel watermarking technique using combinational spatial and frequency domains is presented. In order to correct rounding errors, a novel technique based on the genetic algorithm (GA) is developed. By separating medical images into Region of Interest (ROI) and non-ROI parts, higher compression rates can be achieved where the ROI is compressed by lossless compression and the non-ROI by lossy compression. The GA-based watermarking technique can also be considered as a fundamental platform for other fragile watermarking techniques. In order to simplify the selection and integrate different watermarking techniques, a novel adjusted-purpose digital watermarking is developed. In order to enlarge the capacity of robust watermarking, a novel robust high-capacity watermarking is developed. In steganographic system, a novel steganographic algorithm is developed by using GA to break the inspection of steganalytic system. In morphological processing, the GA-based techniques are developed to decompose arbitrary shapes of big binary structuring elements and arbitrary values of big grayscale structuring elements into small ones. The decomposition is suited for a parallel-pipelined architecture. The techniques can speed up the morphological processing and allow full freedom for users to design any type and any size of binary and grayscale structuring elements. In applications such as shortest path planning, a novel method is first presented to obtaining Euclidean distance transformation (EDT) in just two scans of image. The shortest path can be extracted based on distance maps by tracking minimum values. In order to record the motion path, a new chain-code representation is developed to allow forward and backward movements. By placing the smooth turning-angle constraint, it is possible to mimic realistic motions of cars. By using dynamically rotational morphology, it is not only guarantee collision-free in the shortest path, but also reduce time complexity dramatically. As soon as the distance map of a destination and collision-free codes have been established off-line, shortest paths of cars given any starting location toward the destination can be promptly obtained on-line