Linear Image Reconstruction from a Sparse Set of alpha-Scale Space Features by Means of Inner Products of Sobolev Type
نویسندگان
چکیده
Inner products of Sobolev type are extremely useful for image reconstruction of images from a sparse set of -scale space features. The common (non)-linear reconstruction frameworks, follow an Euler Lagrange minimization. If the Lagrangian (prior) is a norm induced by an inner product of a Hilbert space, this Euler Lagrange minimization boils down to a simple orthogonal projection within the corresponding Hilbert space. This basic observation has been overlooked in image analysis for the cases where the Lagrangian equals a norm of Sobolev type, resulting in iterative (non-linear) numerical methods, where already an exact solution with non-iterative linear algorithm is at hand. Therefore we provide a general theory on linear image reconstructions and metameric classes of images. By applying this theory we obtain visually more attractive reconstructions than the previously proposed linear methods and we nd connected curves in the metameric class of images, determined by a xed set of linear features, with a monotonic increase of smoothness. Although the theory can be applied to any linear feature reconstruction or principle component analysis, we mainly focus on reconstructions from so-called topological features (such as top-points and grey-value ux) in scale space, obtained from geometrical observations in the deep structure of a scale space.
منابع مشابه
Hyperspectral Image Classification Based on the Fusion of the Features Generated by Sparse Representation Methods, Linear and Non-linear Transformations
The ability of recording the high resolution spectral signature of earth surface would be the most important feature of hyperspectral sensors. On the other hand, classification of hyperspectral imagery is known as one of the methods to extracting information from these remote sensing data sources. Despite the high potential of hyperspectral images in the information content point of view, there...
متن کاملFast Reconstruction of SAR Images with Phase Error Using Sparse Representation
In the past years, a number of algorithms have been introduced for synthesis aperture radar (SAR) imaging. However, they all suffer from the same problem: The data size to process is considerably large. In recent years, compressive sensing and sparse representation of the signal in SAR has gained a significant research interest. This method offers the advantage of reducing the sampling rate, bu...
متن کاملSparse Structured Principal Component Analysis and Model Learning for Classification and Quality Detection of Rice Grains
In scientific and commercial fields associated with modern agriculture, the categorization of different rice types and determination of its quality is very important. Various image processing algorithms are applied in recent years to detect different agricultural products. The problem of rice classification and quality detection in this paper is presented based on model learning concepts includ...
متن کاملOptic Flow from Dynamic Anchor Point Attributes
Optic flow describes the apparent motion that is present in an image sequence. We show the feasibility of obtaining optic flow from dynamic properties of a sparse set of so called anchor points. Singular points of a Gaussian scale space image are identified as feasible anchor point candidates and analytical expressions describing their dynamic properties are presented. The advantage of approach...
متن کاملRice Classification and Quality Detection Based on Sparse Coding Technique
Classification of various rice types and determination of its quality is a major issue in the scientific and commercial fields associated with modern agriculture. In recent years, various image processing techniques are used to identify different types of agricultural products. There are also various color and texture-based features in order to achieve the desired results in this area. In this ...
متن کامل