228 research outputs found
Contains and Inside relationships within combinatorial Pyramids
Irregular pyramids are made of a stack of successively reduced graphs
embedded in the plane. Such pyramids are used within the segmentation framework
to encode a hierarchy of partitions. The different graph models used within the
irregular pyramid framework encode different types of relationships between
regions. This paper compares different graph models used within the irregular
pyramid framework according to a set of relationships between regions. We also
define a new algorithm based on a pyramid of combinatorial maps which allows to
determine if one region contains the other using only local calculus.Comment: 35 page
Integration of SAR and DEM data: Geometrical considerations
General principles for integrating data from different sources are derived from the experience of registration of SAR images with digital elevation models (DEM) data. The integration consists of establishing geometrical relations between the data sets that allow us to accumulate information from both data sets for any given object point (e.g., elevation, slope, backscatter of ground cover, etc.). Since the geometries of the two data are completely different they cannot be compared on a pixel by pixel basis. The presented approach detects instances of higher level features in both data sets independently and performs the matching at the high level. Besides the efficiency of this general strategy it further allows the integration of additional knowledge sources: world knowledge and sensor characteristics are also useful sources of information. The SAR features layover and shadow can be detected easily in SAR images. An analytical method to find such regions also in a DEM needs in addition the parameters of the flight path of the SAR sensor and the range projection model. The generation of the SAR layover and shadow maps is summarized and new extensions to this method are proposed
Invariant Representative Cocycles of Cohomology Generators using Irregular Graph Pyramids
Structural pattern recognition describes and classifies data based on the
relationships of features and parts. Topological invariants, like the Euler
number, characterize the structure of objects of any dimension. Cohomology can
provide more refined algebraic invariants to a topological space than does
homology. It assigns `quantities' to the chains used in homology to
characterize holes of any dimension. Graph pyramids can be used to describe
subdivisions of the same object at multiple levels of detail. This paper
presents cohomology in the context of structural pattern recognition and
introduces an algorithm to efficiently compute representative cocycles (the
basic elements of cohomology) in 2D using a graph pyramid. An extension to
obtain scanning and rotation invariant cocycles is given.Comment: Special issue on Graph-Based Representations in Computer Visio
Open Issues and Chances for Topological Pyramids
High resolution image data require a huge
amount of computational resources. Image pyramids
have shown high performance and flexibility to reduce
the amount of data while preserving the most relevant
pieces of information, and still allowing fast access to
those data that have been considered less important before.
They are able to preserve an existing topological structure
(Euler number, homology generators) when the spatial
partitioning of the data is known at the time of construction.
In order to focus on the topological aspects let us call this
class of pyramids “topological pyramids”. We consider
here four open problems, under the topological pyramids
context: The minimality problem of volumes representation,
the “contact”-relation representation, the orientation of
gravity and time dimensions and the integration of different
modalities as different topologies.Austrian Science Fund P20134-N13Junta de Andalucía FQM–296Junta de Andalucía PO6-TIC-0226
Irregular graph pyramids and representative cocycles of cohomology generators
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed
Image = Structure + Few Colors
Topology plays an important role in computer vision by capturing
the structure of the objects. Nevertheless, its potential applications
have not been sufficiently developed yet. In this paper, we combine the
topological properties of an image with hierarchical approaches to build a
topology preserving irregular image pyramid (TIIP). The TIIP algorithm
uses combinatorial maps as data structure which implicitly capture the
structure of the image in terms of the critical points. Thus, we can achieve
a compact representation of an image, preserving the structure and topology
of its critical points (maxima, the minima and the saddles). The parallel
algorithmic complexity of building the pyramid is O(log d) where d is
the diameter of the largest object.We achieve promising results for image
reconstruction using only a few color values and the structure of the image,
although preserving fine details including the texture of the image
LBP and irregular graph pyramids
In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes the topological category (local max, min, slope, saddle) of the gray level landscape around the center region. Given a 2D grayscale image I, our goal is to obtain a simplified image which can be seen as “minimal” representation in terms of topological characterization of I. For this, a method is developed based on merging regions and Minimum Contrast Algorithm
Cubical Cohomology Ring of 3D Photographs
Cohomology and cohomology ring of three-dimensional (3D) objects are
topological invariants that characterize holes and their relations. Cohomology
ring has been traditionally computed on simplicial complexes. Nevertheless,
cubical complexes deal directly with the voxels in 3D images, no additional
triangulation is necessary, facilitating efficient algorithms for the
computation of topological invariants in the image context. In this paper, we
present formulas to directly compute the cohomology ring of 3D cubical
complexes without making use of any additional triangulation. Starting from a
cubical complex that represents a 3D binary-valued digital picture whose
foreground has one connected component, we compute first the cohomological
information on the boundary of the object, by an incremental
technique; then, using a face reduction algorithm, we compute it on the whole
object; finally, applying the mentioned formulas, the cohomology ring is
computed from such information
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