Scale Space

We present an energy based approach to estimate a dense disparity map between two images while preserving its discontinuities resulting from image boundaries. We first derive a simpli#ed expression for the disparity that allows us to easily estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scale-space. We prove the existence and uniqueness of the underlying parabolic partial differential equation. Experimental results ...

Bu makale en iyi çalışan özellik çıkarımı (feature extraction) yöntemlerinden biri olan boyut ile
değişmeyen özellik çıkarımı (SIFT) yöntemi ve bu yöntemin eşleştirme (matching) yeteneğinin
kapasitesi incelenmiştir. Bu bağlamda karşılaştırılan resimlerdeki eşleşmesi beklenen nesnelerin
farklı boyutlarda, farklı açılarda, farklı aydınlanma seviyeleri, farklı gürültü seviyelerinde ve farklı
çözünürlük değerlerinde denenerek beklenen sonuçları verdiği gösterilmiştir. Bu yöntemde
çıkarılan özelliklerin (feature) ayırt ediciliği yüksek oranda ve güvenilirdir. SIFT kullanılarak
nesne tanıma gerçekleştirilebileceği gibi resimlerin 2b ve 3b birleştirilmesi (reconstruction)
alanında da kullanılmaktadır.

A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.

... A novel result is that a fruitful way of doing this is to build scale paths from coarse ... edge, which has become diffuser due to smoothing (blurring) the image in such a way that it ... From a pedagogic point of view, we prefer the word Gaussian differences to normalized gradient magni ...

This paper presents an automatic multiple-scale algorithm for delineation of individual tree crowns in high spatial resolution infrared colour aerial images. The tree crown contours were identified as zero-crossings, with convex grey-level curvature, which were computed on the intensity image for each image scale. A modified centre of curvature was estimated for every edge segment pixel. For each segment, these centre points formed a swarm which was modelled as a primal sketch using an ellipse extended with the mean circle of curvature. The model described the region of the derived tree crown based on the edge segment at the current scale. The sketch was rescaled with a significance value and accumulated for a scale interval. In the accumulated sketch, a tree crown segment was grown, starting at local peaks, under the condition that it was inside the area of healthy vegetation in the aerial image and did not trespass into a neighbouring crown segment. The method was evaluated by comparison with manual delineation and with ground truth on 43 randomly selected sample plots. It was concluded that the performance of the method is almost equivalent to visual interpretation. On the average, seven out of ten tree crowns were the same. Furthermore, ground truth indicated a large number of hidden trees. The proposed technique could be used as a basic tool in forest surveys.

This paper presents the fusion of monogenic signal process- ing and dierential geometry to enable monogenic analyzing of local intrinsic 2D features of low level image data. New rotational invariant features such like structure and geometry (angle of intersection) of two superimposed intrinsic 1D signals will be extracted without the need of any steerable filters. These features are important for

We describe a nonparametric framework for incorporating information from co-registered anatomical images into positron emission tomographic (PET) image reconstruction through priors based on information theoretic similarity measures. We compare and evaluate the use of mutual information (MI) and joint entropy (JE) between feature vectors extracted from the anatomical and PET images as priors in PET reconstruction. Scale-space theory provides a framework for the analysis of images at different levels of detail, and we use this approach to define feature vectors that emphasize prominent boundaries in the anatomical and functional images, and attach less importance to detail and noise that is less likely to be correlated in the two images. Through simulations that model the best case scenario of perfect agreement between the anatomical and functional images, and a more realistic situation with a real magnetic resonance image and a PET phantom that has partial volumes and a smooth varia...

In this work, a multi-channel model for image representation is derived based on the scale-space theory. This model is inspired in biological insights and it includes some important properties of human vision such as the Gaussian derivative model for early vision proposed by Young. The image transform that we propose in this work uses similar analysis operators as the Hermite

The dynamics of ecological systems include a bewildering number of biotic interactions that unfold over a vast range of spatial scales. Here, employing simple and general empirical arguments concerning the nature of movement, trophic position and behaviour we outline a general theory concerning the role of space and food web structure on food web stability. We argue that consumers link food webs in space and that this spatial structure combined with relatively rapid behavioural responses by consumers can strongly influence the dynamics of food webs. Employing simple spatially implicit food web models, we show that large mobile consumers are inordinately important in determining the stability, or lack of it, in ecosystems. More specifically, this theory suggests that mobile higher order organisms are potent stabilizers when embedded in a variable, and expansive spatial structure. However, when space is compressed and higher order consumers strongly couple local habitats then mobile consumers can have an inordinate destabilizing effect. Preliminary empirical arguments show consistency with this general theory.

In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 565–593) can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in different images, (ii) use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diffusion–reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the optical flow methods with 100 % density that are evaluated by Barron et al. (1994, Int. J. Comput. Vision, Vol. 12, pp. 43–47). Our software is available from the Internet.