Globally Aligned Spatial Distribution (GASD) descriptors
This document describes the Globally Aligned Spatial Distribution ([GASD]) global descriptor to be used for efficient object recognition and pose estimation.
GASD is based on the estimation of a reference frame for the whole point cloud that represents an object instance, which is used for aligning it with the canonical coordinate system. After that, a descriptor is computed for the aligned point cloud based on how its 3D points are spatially distributed. Such descriptor may also be extended with color distribution throughout the aligned point cloud. The global alignment transforms of matched point clouds are used for computing object pose. For more information please see [GASD].
Theoretical primer
The Globally Aligned Spatial Distribution (or GASD) global description method takes as input a 3D point cloud that represents a partial view of a given object. The first step consists in estimating a reference frame for the point cloud, which allows the computation of a transform that aligns it to the canonical coordinate system, making the descriptor pose invariant. After alignment, a shape descriptor is computed for the point cloud based on the spatial distribution of the 3D points. Color distribution along the point cloud can also be taken into account for obtaining a shape and color descriptor with a higher discriminative power. Object recognition is then performed by matching query and train descriptors of partial views. The pose of each recognized object is also computed from the alignment transforms of matched query and train partial views.
The reference frame is estimated using a Principal Component Analysis (PCA) approach. Given a set of 3D points
System Message: WARNING/2 (\boldsymbol{P_i})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (i\in\{1, ..., n\})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{\overline{P}})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{C})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{P_i})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{\overline{P}})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{C}=\frac{1}{n}\sum_{i=1}^{n}(\boldsymbol{P_i}-\boldsymbol{\overline{P}})(\boldsymbol{P_i}-\boldsymbol{\overline{P}})^T.)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.After that, the eigenvalues
System Message: WARNING/2 (\lambda_j)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{v_j})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{C})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (j\in\{1, 2, 3\})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{C}\boldsymbol{v_j}=\lambda_j\boldsymbol{v_j})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{v_1})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (z)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{v_1})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 ([-90^{\circ}, 90^{\circ}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{v_1})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (z)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (x)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{v_3})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (y)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{v_2}=\boldsymbol{v_1}\times\boldsymbol{v_3})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.From the reference frame, it is possible to compute a transform
System Message: WARNING/2 ([\boldsymbol{R} | \boldsymbol{t}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\boldsymbol{P_i})
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 ([\boldsymbol{R} | \boldsymbol{t}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\begin{bmatrix} \boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1 \end{bmatrix}= \begin{bmatrix} \boldsymbol{v_3}^T & -\boldsymbol{v_3}^T\boldsymbol{\overline{P}} \\ \boldsymbol{v_2}^T & -\boldsymbol{v_2}^T\boldsymbol{\overline{P}} \\ \boldsymbol{v_1}^T & -\boldsymbol{v_1}^T\boldsymbol{\overline{P}} \\ \boldsymbol{0} & 1 \end{bmatrix}.)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.Once the point cloud is aligned using the reference frame, a pose invariant global shape descriptor can be computed from it. The point cloud axis-aligned bounding cube centered on the origin is divided into an
System Message: WARNING/2 (m_s \times m_s \times m_s)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_s)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_s=1)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_s>1)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.The contribution of each sample to the histogram is normalized with respect to the total number of points in the cloud. Optionally, interpolation may be used to distribute the value of each sample into adjacent cells, in an attempt to avoid boundary effects that may cause abrupt changes to the histogram when a sample shifts from being within one cell to another. The descriptor is then obtained by concatenating the computed histograms.


Color information can also be incorporated to the descriptor in order to increase its discriminative power. The color component of the descriptor is computed with an
System Message: WARNING/2 (m_c \times m_c \times m_c)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_c)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.Query and train descriptors are matched using a nearest neighbor search approach. After that, for each matched object instance, a coarse pose is computed using the alignment transforms obtained from the reference frames of the respective query and train partial views. Given the transforms
System Message: WARNING/2 ([\mathbf{R_{q}} | \mathbf{t_{q}}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 ([\mathbf{R_{t}} | \mathbf{t_{t}}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 ([\mathbf{R_{c}} | \mathbf{t_{c}}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\begin{bmatrix} \mathbf{R_{c}} & \mathbf{t_{c}} \\ \mathbf{0} & 1 \end{bmatrix}= {\begin{bmatrix} \mathbf{R_{q}} & \mathbf{t_{q}} \\ \mathbf{0} & 1 \end{bmatrix}}^{-1} \begin{bmatrix} \mathbf{R_{t}} & \mathbf{t_{t}} \\ \mathbf{0} & 1 \end{bmatrix}.)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.The coarse pose
System Message: WARNING/2 ([\mathbf{R_{c}} | \mathbf{t_{c}}])
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.Estimating GASD features
The Globally Aligned Spatial Distribution is implemented in PCL as part of the pcl_features library.
The default values for color GASD parameters are:
System Message: WARNING/2 (m_s=6)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_s=1)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (m_c=4)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_c=12)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (m_s=8)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (l_s=1)
latex exited with error [stdout] This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, romanian, rus sian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turkish, ukenglis h, ukrainian, uppersorbian, welsh, loaded. (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.128 \endinput ^^M No pages of output. Transcript written on math.log.The following code snippet will estimate a GASD shape + color descriptor for an input colored point cloud.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | #include <pcl/point_types.h>
#include <pcl/features/gasd.h>
{
pcl::PointCloud<pcl::PointXYZRGBA>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZRGBA>);
... read, pass in or create a point cloud ...
// Create the GASD estimation class, and pass the input dataset to it
pcl::GASDColorEstimation<pcl::PointXYZRGBA, pcl::GASDSignature984> gasd;
gasd.setInputCloud (cloud);
// Output datasets
pcl::PointCloud<pcl::GASDSignature984> descriptor;
// Compute the descriptor
gasd.compute (descriptor);
// Get the alignment transform
Eigen::Matrix4f trans = gasd.getTransform (trans);
// Unpack histogram bins
for (size_t i = 0; i < size_t( descriptor[0].descriptorSize ()); ++i)
{
descriptor[0].histogram[i];
}
}
|
The following code snippet will estimate a GASD shape only descriptor for an input point cloud.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | #include <pcl/point_types.h>
#include <pcl/features/gasd.h>
{
pcl::PointCloud<pcl::PointXYZ>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZ>);
... read, pass in or create a point cloud ...
// Create the GASD estimation class, and pass the input dataset to it
pcl::GASDEstimation<pcl::PointXYZ, pcl::GASDSignature512> gasd;
gasd.setInputCloud (cloud);
// Output datasets
pcl::PointCloud<pcl::GASDSignature512> descriptor;
// Compute the descriptor
gasd.compute (descriptor);
// Get the alignment transform
Eigen::Matrix4f trans = gasd.getTransform (trans);
// Unpack histogram bins
for (size_t i = 0; i < size_t( descriptor[0].descriptorSize ()); ++i)
{
descriptor[0].histogram[i];
}
}
|
[GASD] | (1, 2) http://www.cin.ufpe.br/~jpsml/uploads/8/2/6/7/82675770/pid4349755.pdf |
Note
@InProceedings{Lima16SIBGRAPI, author = {Joao Paulo Lima and Veronica Teichrieb}, title = {An Efficient Global Point Cloud Descriptor for Object Recognition and Pose Estimation}, booktitle = {Proceedings of the 29th SIBGRAPI - Conference on Graphics, Patterns and Images}, year = {2016}, address = {Sao Jose dos Campos, Brazil}, month = {October} }