Possibility of practical application of algorithmic probability is analyzed on an example of image inpainting problem that precisely corresponds to the prediction problem. Such consideration is fruitful both for the theory of universal prediction and practical image inpaiting methods. Efficient application of algorithmic probability implies that its computation is essentially optimized for some specific data representation. In this paper, we considered one image representation, namely spectral representation, for which an image inpainting algorithm is proposed based on the spectrum entropy criterion. This algorithm showed promising results in spite of very simple representation. The same approach can be used for introducing ALP-based criterion for more powerful image representations.
Learning is one of the most crucial components, which increases generality, flexibility, and robustness of computer
vision systems. At present, image analysis algorithms adopt particular machine learning methods resulting in rather
superficial learning. We present a new paradigm for constructing essentially learnable image analysis algorithms.
Learning is interpreted as optimization of image representations. Notion of representation is formalized within
information-theoretic framework. Optimization criterion is derived from well-known minimum description length
(MDL) principle. Adaptation of the MDL principle in computer vision has been receiving increasing attention. However,
this principle has been applied in heuristic way. We deduced representational MDL (RMDL) principle that fills the gap
between theoretical MDL principle and its practical applications. The RMDL principle gives criteria both for optimal
model selection of a single image within given representation, and for optimal representation selection for an image
sample. Thus, it can be used for optimization of computer vision systems functioning within specific environment.
Adequacy of the RMDL principle was validated on segmentation-based representations applied to different object
domains. A method for learning local features as representation optimization was also developed. This method
outperformed some popular methods with predefined representations such as SURF. Thus, the paradigm can be admitted
The investigation presented in this article continues our long-term efforts directed towards the automatic structural matching of aerospace photographs. An efficient target independent hierarchical structural matching tool was described in our previous paper, which, however, was aimed mostly for the analysis of 2D scenes. It applied the same geometric transformation model to the whole area of image, thus it was nice for the space photographs taken from rather high orbits, but it often failed in the cases when the sensors were positioned near the 3D scenes being observed. Different transformation models should be applied to different parts of images in the last case, and finding a correct separation of image into the areas of homogeneous geometric transformations was the main problem.
Now we succeeded in separating the images of scenes into the surfaces of different objects on the base of their textural and spectral features, thus we have got a possibility of separate matching the sub-images corresponding to such objects applying different transformation model to each such sub-image. Some additional limitations were used in the course of such separation and matching. In particular, the a priory assumptions were applied in different cases about the possible geometry of scenes, rules of illumination and shadowing, thus the aerospace photographs, indoor scenes, or images of aircrafts were analyzed in slightly differing ways. However the additional limitations applied could be considered as very general and are worth to be used in a wide sphere of practical tasks. The automatic image analysis was successful in all considered practical cases.
The aim of investigation consists in development of a formal image representation, in whose framework the most relevant information can be extracted from images. Constructing the models of images is considered as a task of inductive inference. The conventional criterions for choosing the best model are based on the Bayesian rule. However there is one classical problem of defining the a priori probabilities of models. The generally adopted approach for overcoming this difficulty is to use the Minimum Description Length (MDL) principle. In the task of interpretation of visual scenes the a priori probabilities of realizations of images are assigned by their representation language. In our work we study the hierarchical structural descriptions of images. A problem of selection of alphabet of structural elements is addressed. Such the commonly used structural elements as the straight lines, angles, arcs, and others are considered, and their usage is grounded on the base of the amount of information contained in them. The composite structural elements can be formed within the framework of hierarchical representations. The grouping rules are generally based on some similarities in the elements. Hence the descriptions of these elements contain the positive mutual information. Such the approach permits to proof the usage of these structural elements, to choose rationally their types, and to elaborate a rigorous criterion of grouping. The results of research implemented in the form of computer programs showed the appropriateness of this approach.
This work addresses the problem of pattern recognition as the task of n-dimensional interpolation of the probability density function with subsequent thresholding. Interpolating function that describes given learning data set is treated as a random process. The task is reduced to simultaneous linear equations. The proposed method can be considered as the construction of an RBF neural network with nonstandard transfer function. The transfer function is chosen to minimize energy of the random process spectrum. Applications of the developed algorithm to the task of texture segmentation are given and comparison with alternative approaches is carried out.
We present an approach to automatic sup-pixel precise measurement of the positions and local orientations of the holes and edge peculiarities of complex shapes in a sheet metal. The sub-pixel precision of measurement is reached by means of a model-based image analysis. A correlation based measure is introduced to obtain the measurement results invariant to illumination conditions. The correlation is calculated of the vector models and the brightness gradient field of the image region in which the local object of interest is expected to be found. The vector models are derived from the CAD-descriptions of industrial components. The task is solved in the context of photogrammetric 3D measurements for the quality control in the industrial environment.
Last years we reported at the SPIE conferences the results of development of a hierarchical structural classifier which used the contour structural elements as an input and was designed for matching the aerospace photographs taken in different seasons from different view points, or formed by different kinds of sensors. The aim of this investigation was development of a theoretical approach which could explain the previously described empirical results and could give a proof for the techniques applied in the elaborated algorithms, since many of these techniques were borrowed from the human vision system or were introduced heuristically. The proposed approach is based on the information theory and minimum description length principle (MDL). This principle can be stated in the following way. Such a model of the initial data should be chosen, which gives their shortest description without information losses when the chosen data model is extended with the description of discrepancy between the model and the data or with the description of the random component. In our case the data is a pair of images to be registered. In the task of image matching the images models are extended with the model of their mutual spatial transformation, and such the transformation is chosen which permits to minimize the joint description of a pair of images. To apply the MDL principle the model is introduced which formalizes the image structural description used in the classifier. Consequently, the methods developed earlier were reformulated in the terms of the proposed theoretical approach. As a result, the necessary improvements of the structural classifier were determined which can increase its reliability.
We present an information-theoretic approach to the image interpretation problems. In the context of this approach such tasks as contour extracting, constructing the most informative image features and image matching are described as a single unified problem. Our approach is based primarily on the interpretation of the image (or image set) representation problem as a Minimum Description Length (MDL) problem. The image matching turns out to be a generally adopted method of images alignment by maximization of their mutual information. However, instead of using the pixels intensities themselves a more condensed data representation form can be used to reduce the dimensionality of input data and to extract the invariant information: hierarchical image structural description. Though we developed and successfully applied the information-theoretic approach for the images matching, it can be extended to the other problems, e.g. the changes detection.
The aim of investigation was developing the image registration algorithms dealing with the aerial and cosmic pictures taken in different seasons from differing view points, or formed by differing kinds of sensors (visible, IR, SAR). The task could not be solved using the traditional correlation based approaches, thus we chose the structural juxtaposition of the stable specific details of pictures as the general image matching technique. Structural matching was usually applied in the expert systems where the rather reliable results were based on the target specific algorithms, but our algorithms deal with the aerospace photographs of arbitrary contents for which the application specific approaches could not be used. The chosen form of structural descriptions should provide distinguishing between the similar simple elements in the huge multitudes of image contours, thus the descriptions were made hierarchical: we grouped the contour elements belonging to the separate compact image regions. The structural matching was carried out in two levels: matching the simple elements of every group in the first image with the ones of every group in the second image; matching the groups as the wholes. The top-down links were used to enhance the lower level matching using the higher level matching results.
The aim of investigation was developing the registration algorithms for the aerial and cosmic pictures taken in different seasons from differing viewpoints, formed by differing kinds of sensors (visible, IR, SAR). Structural matching was chosen as the only approach that could manage with the mentioned image differences. In the contrast to the target dependent structural analysis applied in the expert systems we dealt with the images of arbitrary content, thus the rigidity and opacity of landscape objects and the rules of shadowing were the only limitations applied. The simple contour elements corresponding to the objects borders were judged to be a most stable source of structural descriptions in this uncertain situation. However a large amount of similar simple elements produced a high dimensional structural matching task. It decreased the reliability of matching and exponentially increased the computational expenditures. We solved this problem building the hierarchical structural descriptions. We separated the structural elements to the rather small local groups and structurally matched them using the special tree walking algorithms. Two grouping approaches were applied: uniting the elements belonging to a continuous contour line, or uniting the ones situated in a separate compact region. The matching results were reliable both for the multiple season and multiple sensor images. The first approach demonstrates a slightly better precision, while the second one is slightly more robust and flexible, thus it can deal also with the structural elements of other nature: the compact regions formed in result of texture segmentation were also successfully structurally matched.