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GENUS AND DIMENSION OF DIGITAL IMAGES AND THEIR TIME- AND SPACE-EFFICIENT COMPUTATION

VALENTIN E. BRIMKOV, GIORGIO NORDO, RENETA P. BARNEVA, ANGELO MAIMONE
<span title="">2008</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wkp6ef7uxzdjvbwvq2oe42h5xe" style="color: black;">International journal of shape modeling</a> </i> &nbsp;
In the present paper we first propose a linear time constantworking space algorithm for determining the genus of a connected digital image.  ...  The computation is based on a combinatorial relation for digital images that may be of independent interest as well. We also propose definitions of dimension for planar digital images.  ...  As before, by Time and Space Efficient Computation of Dimension It is not hard to see that, similar to counting holes, digital dimension admits time and space-efficient computation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218654308001129">doi:10.1142/s0218654308001129</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ukjqkc2nqbeglpvi3dmq4dkorm">fatcat:ukjqkc2nqbeglpvi3dmq4dkorm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812013228/http://www.giorgionordo.it/lavori/Genus%20and%20dimension%20o%20digital%20images%20and%20their%20time%20and%20space-efficient%20computation.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e2/44/e24445021beaa66d8f55ce03c926216998ad1b4b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218654308001129"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

Page 2227 of Mathematical Reviews Vol. , Issue 92d [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Using these schemes, algorithms are presented that determine whether or not a finite set S of n digital points in a k-dimensional space is a digital line segment, digital hyperplane, or a digital m-flat  ...  of definition of digital line segments and digital arcs, the time complexity for the digital plane recog- nition problem and simplicity, uniformity and generality of all results.”  ... 
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Digital Geometry, a Survey [article]

Li Chen, David Coeurjolly
<span title="2018-07-06">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It also covers recent developments in the applications of digital geometry and topology including image processing, computer vision, and data science.  ...  This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements.  ...  From a computational point of view, several of these methods lead to time optimal algorithms for computing the error-free Euclidean distance transformation (EDT) for d-dimensional binary images [34] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.02222v1">arXiv:1807.02222v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a5q5mhmly5hwfbjgliywabeosi">fatcat:a5q5mhmly5hwfbjgliywabeosi</a> </span>
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A Topological Method of Surface Representation [chapter]

Vladimir Kovalevsky
<span title="">1999</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A new method of representing a surface in the 3D space as a single digitally continuous sequence of faces is described. The method is based on topological properties of quasi-manifolds.  ...  The code of the surface of a three-dimensional object takes much less memory space then the raster representation of the object. The object may be exactly reconstructed from the code.  ...  These records are used for the calculation of the genus and then deleted. Computer Experiments The method of Section 4 was successfully tested on many different 3D images.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-49126-0_10">doi:10.1007/3-540-49126-0_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fjlyaqkuxfcezpyjtiadlxtcke">fatcat:fjlyaqkuxfcezpyjtiadlxtcke</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810121017/http://www.kovalevsky.de/Surf.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4f/25/4f2594834f7d6b1af5eb6ea736f3a3c35c32f315.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-49126-0_10"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Image Processing in Biology Based on the Fractal Analysis [chapter]

Istvn Sztojnov, Daniela Alexandra, Ctlina Popescu, Vasilic Voine
<span title="2009-12-01">2009</span> <i title="InTech"> Image Processing </i> &nbsp;
Here are introduced the necessary notions for the defining of the fractals and their quantitative evaluation and an algorithm for fractal dimension computation based on biofractal contours processing is  ...  The first application is dedicated to the analysis of the particularities of some species from Gentianaceae family, with the purpose of establishing their affiliation to the Gentiana genus, knowing the  ...  be submerged: the line in a plane, the cone in a three dimensional space.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/7059">doi:10.5772/7059</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6kw4sctgmjfufe6eddurg4ay2m">fatcat:6kw4sctgmjfufe6eddurg4ay2m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501203518/https://cdn.intechopen.com/pdfs/6684.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b8/78/b87862aff0bd9c6450ce2873df789af9eaf2198c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/7059"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

The fractal structure of the ventral scales in legless reptiles [article]

Hisham A. Abdel-Aal, M. El Mansori
<span title="2015-01-23">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work we examine the surface construction of 14 snake species, representing five families, and evaluate the fractal dimension for each of the skins (both the dorsal and ventral sides) using three  ...  different computational algorithms.  ...  Rather, they display a common attitude in their dependence on their roughness to occupy a three dimensional space.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.05886v1">arXiv:1501.05886v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/va37fwu2fnch3fpwvhd4w73lem">fatcat:va37fwu2fnch3fpwvhd4w73lem</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191018125411/https://arxiv.org/pdf/1501.05886v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2c/a1/2ca1f5a8ffdc0902ea313a4914c1c26fc214dd3e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.05886v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Classification of CITES-listed and other neotropical Meliaceae wood images using convolutional neural networks

Prabu Ravindran, Adriana Costa, Richard Soares, Alex C. Wiedenhoeft
<span title="2018-03-23">2018</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r7g2xzafrze7jhzts3tizvsi7e" style="color: black;">Plant Methods</a> </i> &nbsp;
Conclusion: The end-to-end trained image classifiers that we present discriminate the woods based on digital images of the transverse surface of solid wood blocks, which are surfaces and images that can  ...  We build and evaluate models to classify the 10 woods at the species and genus levels, with image-level model accuracy ranging from 87.4 to 97.5%, with the strongest performance by the genus-level model  ...  We further wish to acknowledge a number of useful general discussions about computer vision and machine learning for wood identification with John Hermanson.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s13007-018-0292-9">doi:10.1186/s13007-018-0292-9</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/29588649">pmid:29588649</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC5865295/">pmcid:PMC5865295</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lp4mizy43zaulfcfyisq3haoqi">fatcat:lp4mizy43zaulfcfyisq3haoqi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190430064058/https://plantmethods.biomedcentral.com/track/pdf/10.1186/s13007-018-0292-9" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8c/51/8c51d6655c2dd7e3380c2975c7b189af630799a9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s13007-018-0292-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> springer.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5865295" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

A computational approach for Leishmania genus protozoa detection in bone marrow samples from patients with visceral Leishmaniasis

Angélica Isaza-Jaimes, Valmore Bermúdez, Antonio Bravo, Jhoalmis Sierra Castrillo, Juan Diego Hernández Lalinde, Cleiver A Fossi, Anderson Flórez, Johel E Rodríguez
<span title="2021-01-07">2021</span> <i title="Zenodo"> Zenodo </i> &nbsp;
and preserve the edges in the objects contained in the images.  ...  The application of the proposed computational approach to a set of samples of patients with Visceral Leishmaniasis generated a recognition parasite percentage of approximately 80%.  ...  The method is based on transforming the image as a function of its derivatives in a greater dimension space, this transformation in the space of greater dimension represented the solution of the heat equation  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.4426403">doi:10.5281/zenodo.4426403</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dqgujd5dmrf5hpgzo3nmcm555i">fatcat:dqgujd5dmrf5hpgzo3nmcm555i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210114084804/https://zenodo.org/record/4426403/files/21%20A%20computational%20approach%20for%20Leishmania.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6b/3c/6b3c82bcc439f275df2a97102615daa627353373.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.4426403"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> zenodo.org </button> </a>

Algorithms in Digital Geometry Based on Cellular Topology [chapter]

V. Kovalevsky
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
of digital plane segments, computing the curvature of digital curves, filling of interiors of n-dimensional regions (n=2,3,4), labeling of components (n=2,3), computing of skeletons (n=2, 3).  ...  Now we introduce the notion of a thin boundary: Definition TB: The boundary Fr(T,S) of a subset T of an n-dimensional space S is called thin if it contains no n-dimensional cube of 2 n mutually incident  ...  Their cells with dimension 0 (0-cells) are called points, cells of dimension 1 (1-cells) are called cracks (edges), cells of dimension 2 (2-cells) are called pixels (or facets) and that of dimension 3  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30503-3_27">doi:10.1007/978-3-540-30503-3_27</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ndnsl3injveeboqg7ts26srii4">fatcat:ndnsl3injveeboqg7ts26srii4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090920122033/http://www.miszalok.de:80/Lectures/L08_ComputerVision/kovalevski.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d6/27/d6270a83c2c62deb3b561b4ecaa0d3800cda0e89.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30503-3_27"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Is the study of fungal shape still useful?

Ecaterina Fodor
<span title="2018-03-07">2018</span> <i title="MedCrave Group, LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4gdlkjmujbfmtee5i7xgjxp3me" style="color: black;">Journal of Bacteriology &amp; Mycology Open Access</a> </i> &nbsp;
Opinion In the era of molecular tools used in description and identifications of organisms, their shape still can convey a lot of important information on their properties, identity, evolution and interactions  ...  spaces and the information they can convey.  ...  Conflict of interest There is no conflicts to publish our article in this Journal.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15406/jbmoa.2018.06.00180">doi:10.15406/jbmoa.2018.06.00180</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pkzkk5w4eve5xjjutudpxssuci">fatcat:pkzkk5w4eve5xjjutudpxssuci</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427132833/https://medcraveonline.com/JBMOA/JBMOA-06-00180.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/19/d1/19d124c0045275fb616a0377b29b65779910e669.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15406/jbmoa.2018.06.00180"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Sub-Voxel Topology Control for Level-Set Surfaces

Stephan Bischoff, Leif Kobbelt
<span title="">2003</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p2lpq6bugfcqxk44anrm6yki4m" style="color: black;">Computer graphics forum (Print)</a> </i> &nbsp;
Active contour models are an efficient, accurate, and robust tool for the segmentation of 2D and 3D image data.  ...  We also demonstrate the efficiency and robustness of our method.  ...  The force f may depend on various parameters, like time, position in space, curvature of the surface etc.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1467-8659.00674">doi:10.1111/1467-8659.00674</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tdrkfbhh7vhwlllxe2y2rr7b7a">fatcat:tdrkfbhh7vhwlllxe2y2rr7b7a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810164819/http://hyperfun.org/FHF_Log/BichoffKobbelt_SubvoxelEG03.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/54/3d/543de02e653992818607d94634c5e1d6dc264827.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1467-8659.00674"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On the non-uniform complexity of brain connectivity

Gloria Haro, Christophe Lenglet, Guillermo Sapiro, Paul Thompson
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qcepwfkflvg5toaa6fh2alj3b4" style="color: black;">2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro</a> </i> &nbsp;
We show that these high-dimensional spaces may be understood as unions of manifolds of varying dimensions/complexity and densities.  ...  A stratification and manifold learning approach for analyzing High Angular Resolution Diffusion Imaging (HARDI) data is introduced in this paper.  ...  belong to each cluster, see [5] for details on the theory and the very efficient computation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isbi.2008.4541139">doi:10.1109/isbi.2008.4541139</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isbi/HaroLSh08.html">dblp:conf/isbi/HaroLSh08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/njzy4uzou5dhti237amvpfpxja">fatcat:njzy4uzou5dhti237amvpfpxja</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20080221164048/http://www.ima.umn.edu/preprints/dec2007/2183.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e6/24/e6243c4c808b4de2aa1a0768681b84b380842c9f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isbi.2008.4541139"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

COPY MOVE FORGERY DETECTION USING FFT COEFFICIENTS AND MORPHOLOGICAL OPERATIONS

Nancy Sahota
<span title="2018-02-20">2018</span> <i title="IJARCS International Journal of Advanced Research in Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dbwzqwxyw5hn3aantchmoxx65q" style="color: black;">International Journal of Advanced Research in Computer Science</a> </i> &nbsp;
The dimension of the feature space constructed by the feature extraction techniques may be prohibitive, can involve redundant information and can cause the efficiency of a classifier to deteriorate.  ...  [9] presented an efficient method for image retrieval and detection of copy-move forgery and the resultant performance of the same was discussed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26483/ijarcs.v9i1.5255">doi:10.26483/ijarcs.v9i1.5255</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rdjmycrbczhi7j5h6ikx42qj44">fatcat:rdjmycrbczhi7j5h6ikx42qj44</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721183502/http://ijarcs.info/index.php/Ijarcs/article/download/5255/4461" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/4c/bf4c8e2d92d590a05b4ce68fb6fab47146413f14.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26483/ijarcs.v9i1.5255"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Approximate computations with modular curves [article]

Jean-Marc Couveignes, Bas Edixhoven
<span title="2012-05-26">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These approximations are done in polynomial time in the dimension and the required number of significant digits.  ...  key role of approximate computations with modular curves and their Jacobians.  ...  The complex vector spaces S(SL 2 (Z), k) of cuspidal modular forms of weight k are finite dimensional. The dimension grows roughly as k/12.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1205.5896v1">arXiv:1205.5896v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aw2p4jd6rbf4lfyybtlmldk4z4">fatcat:aw2p4jd6rbf4lfyybtlmldk4z4</a> </span>
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Determining different plant leaves' fractal dimensions: a new approach to taxonomical study of plants

Mehmet Bayirli, Selami Selvi, Ugur Cakilcioglu
<span title="2015-01-14">2015</span> <i title="Bangladesh Journals Online (JOL)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nnpbi55cdreplol54icakuwfca" style="color: black;">Bangladesh Journal of Botany</a> </i> &nbsp;
It is now proposed for the first time that there is a relationship between a fractal dimension of the leaf and a surface density of the image and was concluded that together with other measures, the fractal  ...  The values were then confirmed and compared by those obtained from box-counting method and the exponent values of densitydensity correlation function (first time in the literature).  ...  Ekrem Akçiçek and A. Yeliz Aldemir for their valuable comments and contribution at the preparatory phase of the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3329/bjb.v43i3.21593">doi:10.3329/bjb.v43i3.21593</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yxlmdgv2qfbepisls42zjxdalm">fatcat:yxlmdgv2qfbepisls42zjxdalm</a> </span>
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