14,373 research outputs found
Algorithms to automatically quantify the geometric similarity of anatomical surfaces
We describe new approaches for distances between pairs of 2-dimensional
surfaces (embedded in 3-dimensional space) that use local structures and global
information contained in inter-structure geometric relationships. We present
algorithms to automatically determine these distances as well as geometric
correspondences. This is motivated by the aspiration of students of natural
science to understand the continuity of form that unites the diversity of life.
At present, scientists using physical traits to study evolutionary
relationships among living and extinct animals analyze data extracted from
carefully defined anatomical correspondence points (landmarks). Identifying and
recording these landmarks is time consuming and can be done accurately only by
trained morphologists. This renders these studies inaccessible to
non-morphologists, and causes phenomics to lag behind genomics in elucidating
evolutionary patterns. Unlike other algorithms presented for morphological
correspondences our approach does not require any preliminary marking of
special features or landmarks by the user. It also differs from other seminal
work in computational geometry in that our algorithms are polynomial in nature
and thus faster, making pairwise comparisons feasible for significantly larger
numbers of digitized surfaces. We illustrate our approach using three datasets
representing teeth and different bones of primates and humans, and show that it
leads to highly accurate results.Comment: Changes with respect to v1, v2: an Erratum was added, correcting the
references for one of the three datasets. Note that the datasets and code for
this paper can be obtained from the Data Conservancy (see Download column on
v1, v2
Veni Vidi Vici, A Three-Phase Scenario For Parameter Space Analysis in Image Analysis and Visualization
Automatic analysis of the enormous sets of images is a critical task in life
sciences. This faces many challenges such as: algorithms are highly
parameterized, significant human input is intertwined, and lacking a standard
meta-visualization approach. This paper proposes an alternative iterative
approach for optimizing input parameters, saving time by minimizing the user
involvement, and allowing for understanding the workflow of algorithms and
discovering new ones. The main focus is on developing an interactive
visualization technique that enables users to analyze the relationships between
sampled input parameters and corresponding output. This technique is
implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I
conquered." This strategy is inspired by the mathematical formulas of numbering
computable functions and is developed atop ImageJ, a scientific image
processing program. A case study is presented to investigate the proposed
framework. Finally, the paper explores some potential future issues in the
application of the proposed approach in parameter space analysis in
visualization
The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch
Recent and forthcoming advances in instrumentation, and giant new surveys,
are creating astronomical data sets that are not amenable to the methods of
analysis familiar to astronomers. Traditional methods are often inadequate not
merely because of the size in bytes of the data sets, but also because of the
complexity of modern data sets. Mathematical limitations of familiar algorithms
and techniques in dealing with such data sets create a critical need for new
paradigms for the representation, analysis and scientific visualization (as
opposed to illustrative visualization) of heterogeneous, multiresolution data
across application domains. Some of the problems presented by the new data sets
have been addressed by other disciplines such as applied mathematics,
statistics and machine learning and have been utilized by other sciences such
as space-based geosciences. Unfortunately, valuable results pertaining to these
problems are mostly to be found only in publications outside of astronomy. Here
we offer brief overviews of a number of concepts, techniques and developments,
some "old" and some new. These are generally unknown to most of the
astronomical community, but are vital to the analysis and visualization of
complex datasets and images. In order for astronomers to take advantage of the
richness and complexity of the new era of data, and to be able to identify,
adopt, and apply new solutions, the astronomical community needs a certain
degree of awareness and understanding of the new concepts. One of the goals of
this paper is to help bridge the gap between applied mathematics, artificial
intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in
Astronomy, special issue "Robotic Astronomy
A texture based approach to reconstruction of archaeological finds
Reconstruction of archaeological finds from fragments, is a tedious task requiring many hours of work from the archaeologists and restoration personnel. In this paper we present a framework for the full reconstruction of the original objects using texture and surface design information on the sherd. The texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. The confidence of this process is also defined. Feature values are derived from these original and predicted images of pieces. A combination of the feature and confidence values is used to generate an affinity measure of corresponding pieces. The optimization of total affinity gives the best assembly of the piece. Experimental results are presented on real and artificial data
Challenges in identifying and interpreting organizational modules in morphology
Form is a rich concept that agglutinates information about the proportions and topological arrangement of body parts. Modularity is readily measurable in both features, the variation of proportions (variational modules) and the organization of topology (organizational modules). The study of variational modularity and of organizational modularity faces similar challenges regarding the identification of meaningful modules and the validation of generative processes; however, most studies in morphology focus solely on variational modularity, while organizational modularity is much less understood. A possible cause for this bias is the successful development in the last twenty years of morphometrics, and specially geometric morphometrics, to study patters of variation. This contrasts with the lack of a similar mathematical framework to deal with patterns of organization. Recently, a new mathematical framework has been proposed to study the organization of gross anatomy using tools from Network Theory, so‐called Anatomical Network Analysis (AnNA). In this essay, I explore the potential use of this new framework—and the challenges it faces in identifying and validating biologically meaningful modules in morphological systems—by providing working examples of a complete analysis of modularity of the human skull and upper limb. Finally, I suggest further directions of research that may bridge the gap between variational and organizational modularity studies, and discuss how alternative modeling strategies of morphological systems using networks can benefit from each other
Retrieval of 3D polygonal objects based on multiresolution signatures
In this paper we present a method for retrieving 3D polygonal objects by using two sets of multiresolution signatures. Both sets are based on the progressive elimination of object's details by iterative processing of the 3D meshes. The first set, with five parameters, is based on mesh smoothing. This mainly affects an object's surface. The second set, with three parameters, is based on difference volumes after successive mesh erosions and dilations. Characteristic feature vectors are constructed by combining the features at three mesh resolutions of each object. In addition to being invariant to mesh resolution, the feature vectors are invariant to translation, rotation and size of the objects. The method was tested on a set of 40 complex objects with mesh resolutions different from those used in constructing the feature vectors. By using all eight features, the average ranking rate obtained was 1.075: 37 objects were ranked first and only 3 objects were ranked second. Additional tests were carried out to determine the significance of individual features and all combinations. The same ranking rate of 1.075 can be obtained by using some combinations of only three features. © 2011 Springer-Verlag
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