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1、图像处理数学基础Themathematicalprinciplesofimageprocessing(Parti)Digitalimageprocessingtechnologyisverytalltotherequirementofdevelopmentofmathematicalbasis,somenewmethodsconstantlyemerging,thedazzlingmathematicaldeductionformanyexpectationsoffurtherresearch.Aformalscieneeandengineering
2、studenthasalreadyhadamathematicalfoundation,includingcalculus,linearalgebra,andprobabilitytheory.Butwhenitcomestoanalyzingtheprinciplesofsomeimageprocessingalgorithms,itseemsimpossibletostart・Actualquestionsinvolvedmainlyboildowntothefollowingreasons:1)thecalculus,linearalgebra
3、,probabilitytheory,themathematicalfoundationisveryimportant,butnotshowallcontentinthesecourseshavedirectapplicationinimageprocessingalgorithms;2)whenyou'relearningfromimageprocessingandmath,you，renottryingtoestablishtheconnectionbetweenthem;3)somenewmethodsorso-calledtallalgori
4、thmonthebasisofmorethantheabovethreebasicfieldofmathematicscurriculumarediscussed,whichinvoIvesthepartialdifferentialequationsandvariationalmethod,thecomplexfunction,realvariablefunction,functionalanalysis,etc・4)ifyouarenotamathstudent,youwillhavealotofenergytostudyifyouwanttot
5、eachyourselfallthethingsyou'vetalkedabout・Inthesparetime,theauthorcombinesthelearningandpracticeofimageprocessing,andsummarizessomeofthemathematicalprinciplesnecessaryforthestudyofimageprocessing.Thesecontentsmainlyinvolvecalculus,vectoranalysis,fieldtheory,functionalanalysis,p
6、artialdifferentialequation,complexvariablefunction,variationalmethodandsoon.Linearalgebraandprobabilitytheory,whichIthinkisthebasisofcomparison,donotmakemoney・Isummaryandinduction,extractingthesemathcourse,intheresearchofimageprocessingaremostlikelytoencounterthemostneedtoknows
7、omeknowledge,thentakeastep-by-stepapproachtoreorganizethemtogether・Thispaperdiscussestheapplicationofthesemathematicalknowledgebycombiningthedetailedimageprocessingalgorithm・Toestablishabridgebetweenmathematicalknowledgeandimageprocessing・Thisisasummaryofmydailyresearchandstudy
8、,andIdon，thaveaplantopublishit,becausetheTopicisstilla
