Topic
Distance transform
About: Distance transform is a research topic. Over the lifetime, 2886 publications have been published within this topic receiving 59481 citations.
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TL;DR: An end-to-end deep learning framework to predict the interactions of proteins with potential drugs by representing proteins with a two-dimensional distance map from monomer structures and drugs with molecular linear notation, following the visual question answering mode is proposed.
Abstract: Identifying novel drug–protein interactions is crucial for drug
discovery. For this purpose, many machine learning-based methods have been developed
based on drug descriptors and one-dimensional protein sequences. However, protein
sequences cannot accurately reflect the interactions in three-dimensional space.
However, direct input of three-dimensional structure is of low efficiency due to the
sparse three-dimensional matrix, and is also prevented by the limited number of
co-crystal structures available for training. Here we propose an end-to-end deep
learning framework to predict the interactions by representing proteins with a
two-dimensional distance map from monomer structures (Image) and drugs with
molecular linear notation (String), following the visual question answering mode.
For efficient training of the system, we introduce a dynamic attentive convolutional
neural network to learn fixed-size representations from the variable-length distance
maps and a self-attentional sequential model to automatically extract semantic
features from the linear notations. Extensive experiments demonstrate that our model
obtains competitive performance against state-of-the-art baselines on the directory
of useful decoys, enhanced (DUD-E), human and BindingDB benchmark datasets. Further
attention visualization provides biological interpretation to depict highlighted
regions of both protein and drug molecules. When predicting the interaction of proteins with potential drugs, the
protein can be encoded as its one-dimensional sequence or a three-dimensional
structure, which can capture more relevant features of the protein, but also makes
the task to predict the interactions harder. A new method predicts these
interactions using a two-dimensional distance matrix representation of a protein,
which can be processed like a two-dimensional image, striking a balance between the
data being simple to process and rich in relevant structures.
116 citations
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14 Nov 1988TL;DR: The unique feature of this distance transform, that a vector in the distance map is always pointing to the nearest background point, is exploited in several applications, such as the detection of dominant point in digital curves, curve smoothing, computing Dirichlet tessellations and finding convex hulls.
Abstract: The signed Euclidean distance transform described is a modified version of P.E. Danielsson's Euclidean distance transform (1980). The distance transform produces a distance map in which each pixel is a vector of two integer components. If a distance map is created inside the objects, the two integer values of a pixel in the distance map represent the displacements of the pixel from the nearest background point in the x and y directions, respectively. The unique feature of this distance transform, that a vector in the distance map is always pointing to the nearest background point, is exploited in several applications, such as the detection of dominant point in digital curves, curve smoothing, computing Dirichlet tessellations and finding convex hulls. >
115 citations
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21 Oct 2004TL;DR: In this article, a hierarchical per-feature approach is used to compare images and a distance is calculated between query vectors and corresponding low-level feature vectors extracted from the particular image.
Abstract: An improved image retrieval process based on relevance feedback uses a hierarchical (per-feature) approach in comparing images. Multiple query vectors are generated for an initial image by extracting multiple low-level features from the initial image. When determining how closely a particular image in an image collection matches the initial image, a distance is calculated between the query vectors and corresponding low-level feature vectors extracted from the particular image. Once these individual distances are calculated, they are combined to generate an overall distance that represents how closely the two images match. According to other aspects, relevancy feedback received regarding previously retrieved images is used during the query vector generation and the distance determination to influence which images are subsequently retrieved.
113 citations
01 Jan 2000
TL;DR: In this paper, the closest point transform to a manifold on a rectilinear grid in low dimensional spaces is computed by solving the Eikonal equation |∇u| = 1 by the method of characteristics.
Abstract: This paper presents a new algorithm for computing the closest point transform to a manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for all the points in a grid, (or the grid points within a specified distance of the manifold). We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm computes the closest point on and distance to the manifold by solving the Eikonal equation |∇u| = 1 by the method of characteristics. The method of characteristics is implemented efficiently with the aid of computational geometry and polygon/polyhedron scan conversion. The computed distance is accurate to within machine precision. The computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Thus it has optimal computational complexity. Examples are presented for piecewise linear curves in 2D and triangle meshes in 3D. 1 The Closest Point Transform Let u(x), x ∈ R, be the distance from the point x to a manifold S. If dim(S) = n − 1, (for example curves in 2D or surfaces in 3D), then the distance is signed. The orientation of the manifold determines the sign of the distance. One can adopt the convention that the outward normals point in the direction of positive or negative distance. In order for the distance to be well-defined, the manifold must be orientable and have a consistent orientation. A Klein bottle in 3D for example is not orientable. Two concentric circles in 2D have consistent orientations only if the normals of the inner circle point “inward” and the normals of the outer circle point “outward”, or vice-versa. Otherwise the distance would be ill-defined in the region between the circles. For manifolds which are not closed, the distance is ill-defined in any neighborhood of the boundary. However, the distance is well-defined in neighborhoods of the manifold which do not contain the boundary. If dim(S) < n− 1, (for example a set of points in 2D or a curve in 3D), the distance is unsigned, (non-negative).
112 citations
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TL;DR: A skeletonizing procedure is illustrated that is based on the notion of multiple pixels as well as on the use of the 4-distance transform and produces a labeled skeleton, i.e. a skeleton whose adequacy for shape description purposes is generally acknowledged.
Abstract: A skeletonizing procedure is illustrated that is based on the notion of multiple pixels as well as on the use of the 4-distance transform. The set of the skeletal pixels is identified within one sequential raster scan of the picture where the 4-distance transform is stored. Two local conditions, introduced to characterize the multiple pixels are employed. Since the set of the skeletal pixels is at most two pixels wide, the skeleton can be obtained on completion of an additional inspection of the picture, during which time standard removal operations are applied. Besides being correct and computationally convenient, the procedure produces a labeled skeleton, i.e. a skeleton whose adequacy for shape description purposes is generally acknowledged. >
112 citations