(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 1589556, 26149] NotebookOptionsPosition[ 1588635, 26115] NotebookOutlinePosition[ 1588982, 26130] CellTagsIndexPosition[ 1588939, 26127] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Konsultations-\[CapitalUDoubleDot]bung Mikroskopische Bildverarbeitung\ \>", "Subtitle", CellChangeTimes->{{3.5399522051693335`*^9, 3.5399522291846514`*^9}, { 3.540651173908038*^9, 3.5406511798767114`*^9}, {3.5408240052533703`*^9, 3.5408240059564867`*^9}, {3.653939132097823*^9, 3.653939155942219*^9}, { 3.6568768712387204`*^9, 3.6568768789417963`*^9}}, FontWeight->"Bold"], Cell["18. November 2015", "Subsection", CellChangeTimes->{{3.6084497154275656`*^9, 3.6084497246931314`*^9}, { 3.6084497653959956`*^9, 3.6084499152856617`*^9}, {3.60846567557178*^9, 3.608465735556155*^9}, {3.608465766602843*^9, 3.6084658136962914`*^9}, { 3.6247382364574375`*^9, 3.6247383210198765`*^9}, {3.624901133201543*^9, 3.624901133264042*^9}, {3.624911900651054*^9, 3.6249120621635776`*^9}, { 3.6249122043327227`*^9, 3.624912232457183*^9}, {3.6249122902529483`*^9, 3.6249123031902*^9}, {3.6249127217290387`*^9, 3.624912722619647*^9}, { 3.624913788114814*^9, 3.624913818411107*^9}, {3.6551541355683317`*^9, 3.6551543230863953`*^9}, {3.655154422259096*^9, 3.6551544552581377`*^9}, { 3.655154645907864*^9, 3.655154658680175*^9}, {3.655155193098958*^9, 3.655155217344852*^9}, {3.655155771284944*^9, 3.655155930102202*^9}, { 3.6568769466913624`*^9, 3.656876961722516*^9}}], Cell[TextData[StyleBox["Map ist toll, aber mu\[SZ] es wirklich immer Map \ sein?", "Section"]], "Subsection", CellChangeTimes->{{3.606473933379139*^9, 3.6064740005193343`*^9}, { 3.6065748743169155`*^9, 3.6065748804418764`*^9}, {3.6084492786330423`*^9, 3.6084493022580423`*^9}, {3.608467071063244*^9, 3.608467074547597*^9}, { 3.6084796652381363`*^9, 3.6084796729568367`*^9}, {3.6249091969842153`*^9, 3.6249092190462914`*^9}, {3.6249102219332857`*^9, 3.6249102284175367`*^9}, { 3.6249125495604696`*^9, 3.624912558700919*^9}, {3.65514902369057*^9, 3.655149023791245*^9}, {3.656876970550585*^9, 3.6568769747693076`*^9}, { 3.6568792638484077`*^9, 3.6568792695202465`*^9}, {3.6568821640479364`*^9, 3.6568821761729364`*^9}}], Cell[CellGroupData[{ Cell["\<\ Nehmen Sie das Bild zellealginat und untersuchen Sie zun\[ADoubleDot]chst, \ welchen Farbraum, wieviele Kan\[ADoubleDot]le, welche Abmessungen, welches \ Aspektverh\[ADoubleDot]ltnis und welchen Datentyp es aufweist. Untersuchen \ Sie zudem, wieviele Bytes es im Speicher ben\[ODoubleDot]tigt. Wandeln Sie skalaren reellen Bildwerte mittels einer Quadratwurzelfunktion, \ die Sie zun\[ADoubleDot]chst mit Map auf alle Bildelemente anwenden (mit \ Power oder Sqrt). Testen Sie zudem, ob es n\[UDoubleDot]tzlich ist, mit \ ParallelMap zu arbeiten, indem Sie die Laufzeit mit AbsoluteTiming messen. \ Wenden Sie obendrein die Funktion ByteCount auf ihre L\[ODoubleDot]sung an. \[CapitalUDoubleDot]berlegen Sie nun, ob es tats\[ADoubleDot]chlich \ erforderlich ist, die Bildelemente einzeln zu wandeln. Rufen Sie auf Select[Names[\[OpenCurlyDoubleQuote]*\[CloseCurlyDoubleQuote]],MemberQ[\ Attributes[#],Listable]&] und verschaffen Sie sich eine \[CapitalUDoubleDot]bersicht der Ausgabe. Testen Sie mit einer zehnmillionen Elemente gro\[SZ]en Liste reellwertiger \ Zahlen, was schneller geht, die Wurzel per Element oder die Wurzel auf der \ gesamten Liste. F\[UDoubleDot]hren Sie nun die o.g. Anwendung der Quadratwurzelfunktion ohne \ Map aus und vergleichen Sie die Laufzeit, ebenso den ByteCount. Betrachten Sie nunmehr die Funktion ImageApply und l\[ODoubleDot]sen Sie das \ o.g. Problem damit. Stellen Sie wiederum Laufzeit- und \ Speicherbedarfsbetrachtungen an. Untersuchen Sie, ob das Problem auch mit ImageAdjust l\[ODoubleDot]sbar w\ \[ADoubleDot]re. Stellen Sie alle o.g. Betrachtungen auch f\[UDoubleDot]r das Bild tiffany an. Schlie\[SZ]en Sie ab mit einem selbstgew\[ADoubleDot]hlten Beispiel, wo Sie \ ohne Map nicht auskommen k\[ODoubleDot]nnen.\ \>", "Subsection", CellChangeTimes->{{3.6084497154275656`*^9, 3.6084497246931314`*^9}, { 3.6084497653959956`*^9, 3.6084499152856617`*^9}, {3.60846567557178*^9, 3.608465735556155*^9}, {3.608465766602843*^9, 3.6084658136962914`*^9}, { 3.6247382364574375`*^9, 3.6247383210198765`*^9}, {3.624901133201543*^9, 3.624901133264042*^9}, {3.624911900651054*^9, 3.6249120621635776`*^9}, { 3.6249122043327227`*^9, 3.624912232457183*^9}, {3.6249122902529483`*^9, 3.6249123031902*^9}, {3.6249127217290387`*^9, 3.624912722619647*^9}, { 3.624913788114814*^9, 3.624913818411107*^9}, {3.6551541355683317`*^9, 3.6551543230863953`*^9}, {3.655154422259096*^9, 3.6551544552581377`*^9}, { 3.655154645907864*^9, 3.655154658680175*^9}, {3.655155193098958*^9, 3.655155217344852*^9}, {3.655155771284944*^9, 3.655155930102202*^9}, 3.656876978675533*^9, {3.6568772152677684`*^9, 3.6568772914860306`*^9}, { 3.6568779096695747`*^9, 3.656877961809866*^9}, 3.656878070309171*^9, { 3.6568781344337606`*^9, 3.656878145761813*^9}, {3.656878264432929*^9, 3.656878296932721*^9}, {3.656879277410821*^9, 3.656879322316783*^9}, { 3.6568793862382493`*^9, 3.6568793981912975`*^9}, {3.656879451534706*^9, 3.656879457972165*^9}, {3.6568795274404707`*^9, 3.656879623017984*^9}, { 3.6568796838144693`*^9, 3.656879848032169*^9}, {3.6568798872819176`*^9, 3.6568799282035303`*^9}, {3.6568800923431053`*^9, 3.6568801023742905`*^9}, {3.65688071266726*^9, 3.656880784104303*^9}, { 3.6568811803643117`*^9, 3.6568811986934924`*^9}, {3.6568820406885614`*^9, 3.6568820750791864`*^9}, {3.6568821930635056`*^9, 3.6568822008759556`*^9}, {3.6568823260782795`*^9, 3.656882340640686*^9}, { 3.656884659985217*^9, 3.6568846933287535`*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.656884362533996*^9}] }, Open ]], Cell[TextData[{ StyleBox["K\[ODoubleDot]nnen wir die Bildg\[UDoubleDot]te vergleichend \ messen? Und wie? Mit PSNR (Spitzen-Signal-Rausch-Verh\[ADoubleDot]ltnis)! Und \ via MSE (mittlerer quadratischer Abweichung). Wir betrachten das Bildpaar I \ und K:\n\n", "Section"], Cell[BoxData[ FormBox[ RowBox[{"PSNR", "=", " ", RowBox[{ RowBox[{"10", "*", RowBox[{"Log10", "[", StyleBox[ FractionBox[ SubsuperscriptBox["I", "max", "2"], "MSE"], FontSize->24], "]"}], "dB", " ", "mit", " ", "MSE"}], "=", RowBox[{ FractionBox["1", RowBox[{"m", "\[CenterDot]", "n"}]], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "m"], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "n"], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"I", "(", RowBox[{"i", ",", "j"}], ")"}], "-", RowBox[{"K", "(", RowBox[{"i", ",", "j"}], ")"}]}], ")"}], "2"]}]}]}]}]}], TraditionalForm]]] }], "Subsection", CellChangeTimes->{{3.606473933379139*^9, 3.6064740005193343`*^9}, { 3.6065748743169155`*^9, 3.6065748804418764`*^9}, {3.6084492786330423`*^9, 3.6084493022580423`*^9}, {3.608467071063244*^9, 3.608467074547597*^9}, { 3.6084796652381363`*^9, 3.6084796729568367`*^9}, {3.6249091969842153`*^9, 3.6249092190462914`*^9}, {3.6249102219332857`*^9, 3.6249102284175367`*^9}, { 3.6249125495604696`*^9, 3.624912558700919*^9}, {3.65514902369057*^9, 3.655149023791245*^9}, {3.656876970550585*^9, 3.6568769747693076`*^9}, { 3.6568792638484077`*^9, 3.6568792695202465`*^9}, {3.6568821640479364`*^9, 3.6568821761729364`*^9}, {3.656883457711662*^9, 3.6568835235862403`*^9}, { 3.656883555929783*^9, 3.656883557382899*^9}, {3.6568836165387707`*^9, 3.6568836288511915`*^9}, {3.6568836606009884`*^9, 3.6568837668034334`*^9}, { 3.6568838019438334`*^9, 3.656884005442531*^9}}], Cell[CellGroupData[{ Cell["\<\ Implementieren Sie diese Berechnung und setzen Sie diese f\[UDoubleDot]r das \ oben erzeugte Bildpaar aus zellealginat ein. \[CapitalUDoubleDot]berlegen Sie, was Sie ggf. modifizieren \ m\[UDoubleDot]ssen, um auch auf Farbbildern arbeiten zu k\[ODoubleDot]nnen. Erzeugen Sie sich eine tempor\[ADoubleDot]re Instanz eines JPEG-komprimierten \ Bildes: ColorConvert[ImportString[ExportString[zellealginat,\[CloseCurlyDoubleQuote]\ JPEG\[CloseCurlyDoubleQuote],\[CloseCurlyDoubleQuote]CompressionLevel\ \[CloseCurlyDoubleQuote]\[Rule]1.0],\[CloseCurlyDoubleQuote]JPEG\ \[CloseCurlyDoubleQuote]],ImageColorSpace[zellealginat]] Vergleichen Sie mittels ihrer PSNR-Berechnung dieses Ergebnis mit dem Original. \ \>", "Subsection", CellChangeTimes->{ 3.6568825657017455`*^9, {3.6568840348798428`*^9, 3.656884125473013*^9}, { 3.6568842528784475`*^9, 3.656884257065921*^9}, {3.6568843659402237`*^9, 3.6568844008462505`*^9}, {3.6568844490490675`*^9, 3.656884462970853*^9}, { 3.6568845968293715`*^9, 3.656884601282468*^9}, {3.6568866300737734`*^9, 3.6568867197606993`*^9}, {3.656914153362033*^9, 3.656914172606387*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.656885500888314*^9}], Cell[BoxData[ RowBox[{ RowBox[{"$HistoryLength", "=", "0"}], 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