Note on Artificial Deformation in Object Shapes Due to Pixelization

Hamana Takashi; Miyazaki Satoshi

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Note on Artificial Deformation in Object Shapes Due to Pixelization

机译：关于像素化导致的物体形状的人工变形的注意事项

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Wequalitativelyexaminethepropertiesofartificialdeformationintheshapesofobjects(galaxiesandstars)inducedbypixelizationeffects(alsocalledaliasingeffects)usingtoymocksimulationimages.Twocausesoftheseeffectshavebeenrecognized.Oneisaconsequenceofobservingthecontinuousskywithdiscretepixels,whichiscalleda€?firstpixelizationa€?.Theother,calleda€?secondpixelizationa€?,isaconsequenceofresamplingapixelizedimageontoanotherpixelgridwhosecoordinatesarenotperfectlyadjustedtotheinputgrid.Wepayspecialattentiontothelatter,becauseitmightbeapotentialsourceofasystematicnoiseinweak-lensinganalysis.Inparticular,itisfoundthatresamplingwithrotationinducesartificialellipticitiesinobjectshapeshavingaperiodicconcentric-circle-shapedpattern.Ourmajorfindingsareasfollows:(1)Theroot-mean-square(RMS)ofartificialellipticitiesinobjectshapesinducedbythefirstpixelizationeffectcanbeaslargeasRMS$$gtrsim$$10$$^{-2}$$ifthecharacteristicsizeoftheobjects(e.g.,theFWHM)issmallerthantwiceofthepixelsize.However,forlargerobjects,itquicklybecomesverysmall(RMS$$lesssim$$10$$^{-5}$$).(2)Theamplitudeofshapedeformationinducedbythesecondpixelizationeffectdependsontheobjectsize.Italsodependsstronglyontheinterpolationschemeadoptedtocarryoutresamplingandonthegridsizeoftheoutputpixels.TheRMSofellipticitiesinobjectshapesinducedbythesecondpixelizationeffectcanbesuppressedtowellbelow$$10^{-2}$$ifoneadoptsaproperinterpolationscheme(implementedinpopularimageprocessingsoftwares).Wealsodiscusstheimpactofpixelizationeffectsonaweak-lensinganalysis.

机译：Wequalitativelyexaminethepropertiesofartificialdeformationintheshapesofobjects（galaxiesandstars）inducedbypixelizationeffects（alsocalledaliasingeffects）usingtoymocksimulationimages.Twocausesoftheseeffectshavebeenrecognized.Oneisaconsequenceofobservingthecontinuousskywithdiscretepixels，whichiscalleda€firstpixelizationa€.Theother，calleda€secondpixelizationa€，isaconsequenceofresamplingapixelizedimageontoanotherpixelgridwhosecoordinatesarenotperfectlyadjustedtotheinputgrid.Wepayspecialattentiontothelatter，becauseitmightbeapotentialsourceofasystematicnoiseinweak-lensinganalysis.Inparticular，itisfoundthatresamplingwithrotationinducesartificialellipticitiesinobjectshapeshavingaperiodicconcentric的圆shapedpattern.Ourmajorfindingsareasfollows：？？？？（1 ）如果对象（例如FWHM）的特征尺寸小于像素大小的两倍，则由第一个像素化效应引起的对象形状中的人工椭圆率的均方根（RMS）可以大到RMS $$ gtrsim $ 10 $$ ^ {-2} $$。 uicklybecomesverysmall（RMS $$ lesssim $$ 10 $$ ^ { - 5} $$）（2）Theamplitudeofshapedeformationinducedbythesecondpixelizationeffectdependsontheobjectsize.Italsodependsstronglyontheinterpolationschemeadoptedtocarryoutresamplingandonthegridsizeoftheoutputpixels.TheRMSofellipticitiesinobjectshapesinducedbythesecondpixelizationeffectcanbesuppressedtowellbelow $$ 10 ^。{ - 2} $$ ifoneadoptsaproperinterpolationscheme（implementedinpopularimageprocessingsoftwares）.Wealsodiscusstheimpactofpixelizationeffectsonaweak-lensinganalysis。

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《PASJ: Publications of the Astronomical Society of Japan》 |2008年第6期|共页
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Hamana Takashi; Miyazaki Satoshi;
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1. Note on Artificial Deformation in Object Shapes Due to Pixelization [J] . Takashi HAMANA, Satoshi MIYAZAKI PASJ: Publications of the Astronomical Society of Japan . 2008,第6期

机译：关于像素化导致的物体形状的人工变形的注意事项
2. Method to measure 3D deformation using defocused images of objects with artificial speckle features [J] . Qian Jiong, Fang Qin-Zhi, Hu Qinwei, Applied optics . 2018,第8期

机译：使用具有人工斑点特征的物体的离焦图像来测量3D变形的方法
3. Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval [J] . Arun Anand, Vani K Chhaniwal, Percival Almoro, Optics Letters . 2009,第10期

机译：使用体积散斑场和相位检索测量3D对象的形状和变形
4. From partial shape matching through local deformation to robust global shape similarity for object detection [C] . Ma Tianyang, Latecki Longin Jan 2011 IEEE Conference on Computer Vision and Pattern Recognition . 2011

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5. Pixelization, Colorization and Object Localization Using Deep Convolutional Neural Network with Minimal Manual Labeling [D] . Han, Chu. 2019

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7. A note on artificial deformation in object shapes due to the pixelization [O] . Hamana, Takashi, Miyazaki, Satoshi 2008

机译：关于物体形状的人工变形的一个注记马赛克
8. Geometric Methods for ATR: Shape Analysis, Object/Image Metrics, Shape Reconstruction, and Shape Statistics. [R] . Stiller, P. F., Johnson, A. 2011

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Note on Artificial Deformation in Object Shapes Due to Pixelization

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