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Short Assignment Requirements

only questions 2 a ,b ;3 and 4 a , b ,c, d are to be done with clear outputs and m files and explanations.

Assignment Description

Homework 2

Math/InfAs/CprE 535

Spring 2019


On-campus due date: Thursday Feb. 28, 2019

Off-campus due date: Monday, March 4, 2019


Please submit           a          zipped           file,     which contains        all       your   write  up            (including     Problem        1)        and     codes to        Canvas.          Be       sure    to            include          all       images           requested     for       Problem        2-5.     Do       not            include          images           generated     from   Problem        1.         Those will     be            uploaded      to        CyBox.           


1.       Image           Data      Collection.          You        need      two        different              smartphones    as            your        devices for          data       collection:           (You       can         use         your       own       cell         phone   as        Camera               I,             and        borrow another cellphone            for          Camera               II.            For         those        who       don’t      have      access   to            a              second  device,  please   email     Dr.          Newman              at        ..., and        she         will        provide you         with       an           old          cellphone            from        the         lab,         if             you         are         on           campus):            

(1)   Collect          90           JPEG      image    files        from      Camera               I,             and        40           JPEG        images  from      Camera               II.            For         the         90           JPEG      images  from      Camera        I,             make     sure       50           of            them     are         flat-field               images  and        the         rest        40           are         all           natural scene      images.                 For         the         40           images  from        Camera               II,            make     sure       they       are         all           natural-scene     images. AVOID        pictures               of            sensitive              nature: Don’t     have      people  in            your       pictures,        private information        such       as            names,  addresses,           etc.         or            other     pictures        of            an           inappropriate    nature.



(2)   Rename       all           your       images  with       the         following             labeling:             













Example:             Camera_1_iPhone7_flat_1.jpg,     etc.                        


(3)   Record          the         models/types    of            cameras               used      for          your       experiment        and        describe               in            a              short     paragraph           in            your       write     up.         

(4)   Include         a              description         about    how       your       process to            obtain   the         flat-field        images  and        natural-scene    images.


Upload  the         images  you         collect   to            the         Cybox   link        (don’t   upload to            Canvas)               that I              will        share     with       you.                        Each      of            you         will        create   a              folder    in            the Cybox    folder    called                   


yourfirstnameLastinitial_HW2_Images        Example:               




In            that        folder,   create   2             subfolders           called    Camera_1             and        Camera_2.            In            this folder   

(yourfirstnameLastinitial_HW2_Images),              please   also        put         a              .txt         file          or            a boxnote,               where   you         describe               the         two        models of            cameras               you         used      in your       data       collection.                           

In            the         folder    Camera_1,            put         your       50           flat-field               images  from      your camera and        40           natural scene      images. In            the         folder    Camera_2,            put         40 natural scene     pictures               taken     with       Camera_2.          



2.       Implement LSB        replacement.    Your      goal        for          this        problem               is             to            generate        a              stego     image    using     LSB        replacement.                     Be           sure       to            implement          the        algorithm            on           the         pear      and        onion    gray       images in            HW.2_Images    folder.   You        may       use         the         formula in            image    algebra in            the         slides,   or            you         can        develop your       own       approach.                           

What             to            submit: a             function              m-file   that        has         form:    

function       [stego]  =             embedLSB(imagepath,   payloadlength)                  

where           imagepath            is             a              path       to            an           image    file          on           the         computer;        payloadlength     is             50           or            75.          For         the         output, stego      is             the         resulting        stego     image.  


and                a             separate              script    file         to            run         it.           


(a)   Create   an           array     M            the         same     size        as            the         image.   The        matrix  M            will                hold       the         payload or            message               bits.       Generate             random 0s           and        1s                and        store      them     in            the         matrix  M.           Then,     embed  the         top         half        of                the         matrix  M            into        the         first        50%       of            the         least      significant           bits                of            the         cover     image,   lexicographically              (row-wise:          left         to            right,     top                to            bottom of            the         array,    or            column-wise:     top         to            bottom, left         to                right).   This       produces             a              stego     image    –              call         it             stego2a.png        -                whose   payload is             contained            in            the         first        50%       of            the         bits        of                the         cover     image.   (The       remaining           gray       values   of            the         stego     image    are                the         same     as            the         cover     image.)                

(b)   For         the         second  experiment,       do           as            in            part       (a),         but         use         75%       of                M.           Embed  the         top         ¾            of            M            into        the         cover     image,                lexicographically.             This       produces             a              stego     image    –              call         it                stego2b.png       -              whose   payload is             contained            in            the         first        75%       of                the         bits.                      

a.       What     percentage         of            ones       and        zeros     are         in            the         original cover                image    you         used?                   

b.       What     percentage         of            ones       and        zeros     are         in            the         matrix  M?                         

c.        What     percentages       of            ones       and        zeros     are         in            the         top         half        of                M            that        was        written to            stego2a.png?                     

d.       What     percentages       of            ones       and        zeros     are         in            the         top         half        of                M            that        was        written to            stego2b.png?                    

We will        revisit   these     numbers              later.    


3.       Generate     the         p-graph               for          the         two        stego     images generated           from     Problem        2:            You        must      use         the         image    provided              with       the         homework:        pears_gray.png.                Generate             3             stego     images  with       different              embedding         rates        (percentages      of            embedded          bits):     10%,      50%       and        75%.     

The code       chisq.m is             also        provided              in            the         Code      folder    on           Canvas. Run        chisq.m on           your       cover     and        stego     images. Let         j               be           an           integer between        1             and        100,       and        for          a              fixed      image,   lexicographically              read       j%           of        your       stego     image’s gray       values   into        a              column vector.  Pass       this        column vector   ((*,1)        is             a              column vector)  to            chisq.m.               The        variable               in            chisq.m that        stores    the         column vector   is             B.            chisq.m returns a              number between              0             and        1.0,         called    the         p-value  for          that        percentage         of            image    gray       values.  For         an        input     of            j%,          let           𝑝"be       the         number that        chisq.m returns. Do           this        for          every        j               value     from      1             to            100,       and        plot        the         set          of            points   {$𝑗, 𝑝"’:𝑗 = 0, … ,100}.       (Note     that        (0,0)      is             already a              point     on           the         plot.)     That       produces        the         p-graph as            shown   in            class.     It             may       look        very       different              for        different              input     images. You        can         run         different              images  through                chisq.m to        get          an           idea       of            the         different              p-graphs              possible.              Don’t     turn       in        these     extra     runs       though.

Turn              in:           m-file   and        script    to            run         it.            In            your       write-up,             display the        input     image    and        the         3             stego     output  images  and        the         corresponding   p-graphs        for          the         cover     and        stego     images  (you       should  have      4             p-graphs              in            total.                       


4.       Following    the         example               in            class      of            calculating          the         matrix  corresponding   to        the         von         Neumann            template              on           a              3X4        pixel      array     X,            in            this        problem               you         will        create   the         matrix  corresponding   to            a              different        template              on           a              different              sized      array     ,               namely, the         averaging        template.             Display all           matrices              in            your       write     up.          You        may       use         the        computer            to            calculate              the         inverse matrices;             turn       in            all           m-files  used        to            solve      this        problem.             

a.       On  X             =             6x6        array,    write     down     the         36           x              36           matrix  that        corresponds       to            the         averaging            template              on           X,            with       circulant        edges    instead of            truncation.                         

b.       Does              this        matrix  have      an           inverse?               If             so,           calculate              it.                   

c.        Do   the         same     for          the         averaging            template              on           X             =             5x5        array.        What     is             its           inverse, if             it             exists? 

d.       Try this        with       a              few         more     different              sized      arrays   X,            perhaps               even        non-square         arrays.  What     is             your       conjecture           about    which    inverse matrices        you         can         find?      (Hint:    read       the         IA           pdfs.)    


5.       Extra             credit.   For         a              matrix  that        you         can         find        an           inverse, what      are         the        corresponding   template              images?                Can        you         write     a              commutative     diagram        with       corresponding   images  describing           this        relation?              Can        you         display the        template              image    in            the         image    domain?              

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