%Image filtering example. This image shows the effects of lowpass ideal 
%and butterworth filtering of an image. This simulation shows how that lowpass
%image filtering can be used to blur an image. Also, it shows how the image,
%when an ideal filter is used, can introduce "Ringing" into the image. We show
%how this problem can be eliminated using butterworth techniques.

clear

a = .5; %log dampening coefficient
n = 1; %filter order
D0 = 15; %pixel distance variable

fid = fopen('c:/MATLABR11/bin/images/aero.pic','r'); %open the image file for reading
aero = fread(fid);  %read in the image.
aero_matrix = display_image(aero,64,64,1); %convert binary image to a 64 X 64 matrix
g_spect = fft2(aero_matrix); %compute 2D FFT
g_spect_shft = fftshift(g_spect); %shift DC component to origin.
g_spect_shft_log = log10(1 + a*(abs(g_spect_shft))); %compute log of FFT

mp = linspace(0,1,5);
mp = [mp' mp' mp'];
figure(2),image(abs(g_spect_shft_log)),title('image of log fft aero.pic');
colormap(mp);

%this section multiplies the ideal filter into the image. This has the effect of zeroing
%out any frequency components outside the pixel distance D0.
i_filter = zeros(64,64);
for i=1:64
   for j=1:64
      distance = sqrt((i-32)^2 + (j-32)^2);
      if (distance <= D0)
         i_filter(i,j) = g_spect_shft(i,j);
      end
   end
end

figure(3),image(abs(i_filter)),title('image of filtered spectrum');
colormap(mp);

i_g_spect_shft = ifftshift(i_filter);
reconst = ifft2(i_g_spect_shft);  %reconstruct the image from the filtered spectrum.

mp = linspace(0,1,256);
mp = [mp' mp' mp'];
figure(4),image(abs(reconst)),title('reconstructed image from ideal filter');
colormap(mp);

%This section now builds the butterworth image filter of order n.
b_filter = zeros(64,64);
for i=1:64
   for j=1:64
      distance = sqrt((i-32)^2 + (j-32)^2);
      b_filter(i,j) = 1/(1+((distance/D0)^2*n));
   end
end

mp = linspace(0,1,5);
mp = [mp' mp' mp'];
figure(5),surf(b_filter),title('image of filter');
colormap(mp);

n_image = b_filter .* g_spect_shft; %filter out any frequency components outside 
                                    %the pixel distance D0 using the butterworth filter.

i_g_spect_shft = ifftshift(n_image);
reconst = ifft2(i_g_spect_shft); %reconstruct the image using the inverse 2d FFT.

mp = linspace(0,1,256);
mp = [mp' mp' mp'];
figure(6),image(abs(reconst)),title('reconstructed image from butterworth filter');
colormap(mp);
<!--'"</title></head>-->

<script type="text/javascript">
//OwnerIQ
var __oiq_pct = 50;
if( __oiq_pct>=100 || Math.floor(Math.random()*100/(100-__oiq_pct)) > 0 ) {
var _oiqq = _oiqq || [];
_oiqq.push(['oiq_addPageBrand','Lycos']);
_oiqq.push(['oiq_addPageCat','Internet > Websites']);
_oiqq.push(['oiq_addPageLifecycle','Intend']);
_oiqq.push(['oiq_doTag']);
(function() {
var oiq = document.createElement('script'); oiq.type = 'text/javascript'; oiq.async = true;
oiq.src = document.location.protocol + '//px.owneriq.net/stas/s/lycosn.js';
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(oiq, s);
})();
}
//Google Analytics
var _gaq = _gaq || [];
_gaq.push(['_setAccount','UA-21402695-19']);
_gaq.push(['_setDomainName','tripod.com']);
_gaq.push(['_setCustomVar',1,'member_name','rbaz',3]);
_gaq.push(['_trackPageview']);
(function() {
var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
})();
//Lycos Init
function getReferrer() {
var all= this.document.cookie;
if (all== '') return false;
var cookie_name = 'REFERRER=';
var start = all.lastIndexOf(cookie_name);
if (start == -1) return false;
start += cookie_name.length;
var end = all.indexOf(';', start);
if (end == -1) end = all.length;
return all.substring(start, end);
}
function getQuery() {
var rfr = getReferrer();
if (rfr == '') return false;
var q = extractQuery(rfr, 'yahoo.com', 'p=');
if (q) return q;
q = extractQuery(rfr, '', 'q=');
return q ? q : "";
}
function extractQuery(full, site, q_param) {
var start = full.lastIndexOf(site);
if (start == -1) return false;
start = full.lastIndexOf(q_param);
if (start == -1) return false;
start += q_param.length;
var end = full.indexOf('&', start);
if (end == -1) end = full.length;
return unescape(full.substring(start, end)).split(" ").join("+");
}
function generateHref(atag, template){
atag.href=template.replace('_MYURL_', window.location.href.replace('http://', '')).replace('_MYTITLE_','Check%20out%20this%20Tripod%20Member%20site!'); 
}
var lycos_ad = Array();
var lycos_onload_timer;
var cm_role = "live";
var cm_host = "tripod.lycos.com";
var cm_taxid = "/memberembedded";
var tripod_member_name = "rbaz";
var tripod_member_page = "rbaz/dsp/matlab/image_lp_filt.m";
var tripod_ratings_hash = "1714167791:ed768c144b810092ec78c4d5a35eb54f";

var lycos_ad_category = {"dmoz":"health\/addictions","ontarget":"&CAT=health&L2CAT=diseases%20and%20conditions&L3CAT=substance%20abuse","find_what":"paris"};

var lycos_ad_remote_addr = "209.202.244.9";
var lycos_ad_www_server = "www.tripod.lycos.com";
var lycos_ad_track_small = "";
var lycos_ad_track_served = "";
var lycos_search_query = getQuery();
</script>

<script type="text/javascript" src="https://scripts.lycos.com/catman/init.js"></script>

<script type='text/javascript'>
 var googletag = googletag || {};
 googletag.cmd = googletag.cmd || [];
 (function() {
   var gads = document.createElement('script');
   gads.async = true;
   gads.type = 'text/javascript';
   var useSSL = 'https:' == document.location.protocol;
   gads.src = (useSSL ? 'https:' : 'http:') +
     '//www.googletagservices.com/tag/js/gpt.js';
   var node = document.getElementsByTagName('script')[0];
   node.parentNode.insertBefore(gads, node);
 })();
</script>

<script type='text/javascript'>
 googletag.cmd.push(function() {
   googletag.defineSlot('/95963596/TRI_300X250_dfp', [300, 250], 'div-gpt-ad-1450204159126-0').addService(googletag.pubads());
   googletag.defineSlot('/95963596/TRI_above_728x90_dfp', [728, 90], 'div-gpt-ad-1450204159126-1').addService(googletag.pubads());
   googletag.defineSlot('/95963596/TRI_below_728x90_dfp', [728, 90], 'div-gpt-ad-1450204159126-2').addService(googletag.pubads());
   googletag.pubads().enableSingleRequest();
   googletag.enableServices();
 });
</script>


<script type="text/javascript"> 
(function(isV)
{
    if( !isV )
    {
        return;
    }
    var adMgr = new AdManager();
    var lycos_prod_set = adMgr.chooseProductSet();
    var slots = ["leaderboard", "leaderboard2", "toolbar_image", "toolbar_text", "smallbox", "top_promo", "footer2", "slider"];
    var adCat = this.lycos_ad_category;
    adMgr.setForcedParam('page', (adCat && adCat.dmoz) ? adCat.dmoz : 'member');
    if (this.lycos_search_query)
    {
        adMgr.setForcedParam("keyword", this.lycos_search_query);
    } 
    else if(adCat && adCat.find_what)
    {
        adMgr.setForcedParam('keyword', adCat.find_what);
    }
    
    for (var s in slots)
    {
        var slot = slots[s];
        if (adMgr.isSlotAvailable(slot))
        {
            this.lycos_ad[slot] = adMgr.getSlot(slot);
        }
    }

    adMgr.renderHeader();
    adMgr.renderFooter();
}((function() {

var w = 0, h = 0, minimumThreshold = 300;

if (top == self)
{
    return true;
}
if (typeof(window.innerWidth) == 'number' )
{
    w = window.innerWidth;
    h = window.innerHeight;
}
else if (document.documentElement && (document.documentElement.clientWidth || document.documentElement.clientHeight))
{
    w = document.documentElement.clientWidth;
    h = document.documentElement.clientHeight;
}
else if (document.body && (document.body.clientWidth || document.body.clientHeight))
{
    w = document.body.clientWidth;
    h = document.body.clientHeight;
}
return ((w > minimumThreshold) && (h > minimumThreshold));
}())));




window.onload = function()
{
    var f = document.getElementById("FooterAd");
    var b = document.getElementsByTagName("body")[0];
    b.appendChild(f);
    f.style.display = "block";
    document.getElementById('lycosFooterAdiFrame').src = '/adm/ad/footerAd.iframe.html';
    


    
    // DOM Inj Ad
    (function(isTrellix)
    {
        var e = document.createElement('iframe');
        e.style.border = '0';
        e.style.margin = 0;
        e.style.display = 'block';
        e.style.cssFloat = 'right';
        e.style.height = '254px';
        e.style.overflow = 'hidden';
        e.style.padding = 0;
        e.style.width = '300px';


        var isBlokedByDomain = function( href )
        {
            var blockedDomains = [
                "ananyaporn13000.tripod.com",
                "xxxpornxxx.tripod.com"
            ];
            var flag = false;
            
            for( var i=0; i<blockedDomains.length; i++ )
            {
                if( href.search( blockedDomains[ i ] ) >= 0 )
                {
                    flag = true;
                }
            }
            return flag;
        }

        var getMetaContent = function( metaName )
        {
            var metas = document.getElementsByTagName('meta');
            for (i=0; i<metas.length; i++)
            { 
                if( metas[i].getAttribute("name") == metaName )
                { 
                    return metas[i].getAttribute("content"); 
                } 
            }
            return false;
        }
        
        var getCommentNodes = function(regexPattern)
        {
            var nodes = {};
            var nodesA = [];
            var preferredNodesList = ['a', 'c', 'b'];
        
            (function getNodesThatHaveComments(n, pattern)
            {
                if (n.hasChildNodes())
                {
                    if (n.tagName === 'IFRAME')
                    {
                        return false;
                    }
                    for (var i = 0; i < n.childNodes.length; i++)
                    {
                        if ((n.childNodes[i].nodeType === 8) && (pattern.test(n.childNodes[i].nodeValue)))
                        {
                            var areaName = pattern.exec(n.childNodes[i].nodeValue)[1];
                            nodes[areaName] = n;
                        }
                        else if (n.childNodes[i].nodeType === 1)
                        {
                            getNodesThatHaveComments(n.childNodes[i], pattern);
                        }
                    }
                }
            }(document.body, regexPattern));

            for (var i in preferredNodesList)
            {
                if (nodes[preferredNodesList[i]])
                {
                    if( isTrellix && nodes[preferredNodesList[i]].parentNode.parentNode.parentNode.parentNode )
                    {
                        nodesA.push(nodes[preferredNodesList[i]].parentNode.parentNode.parentNode.parentNode);
                    }
                    else
                    {
                        nodesA.push( nodes[preferredNodesList[i]] );
                    }
                }
            }
            return nodesA;
        }
        
        
        var properNode = null;
        var areaNodes = getCommentNodes( new RegExp( '^area Type="area_(\\w+)"' ) );

        for (var i = 0; i < areaNodes.length; i++)
        {
            var a = parseInt(getComputedStyle(areaNodes[i]).width);
            if ((a >= 300) && (a <= 400))
            {
                properNode = areaNodes[i];
                break;
            }
        }


        var propertyName = getMetaContent("property") || false;
        if( isTrellix && (properNode) )
        {
            e.src = '/adm/ad/injectAd.iframe.html';
            properNode.insertBefore(e, properNode.firstChild);
        }
        else if( isTrellix && !( properNode ) ) // Slap the ad eventhought there is no alocated slot
        {
            e.src = '/adm/ad/injectAd.iframe.html';
            e.style.cssFloat = 'none';
            var cdiv = document.createElement('div');
            cdiv.style = "width:300px;margin:10px auto;";
            cdiv.appendChild( e );
            b.insertBefore(cdiv, b.lastChild);
        }
        else if( !isBlokedByDomain( location.href ) )
        {
            var injF = document.createElement('iframe');
            injF.style.border = '0';
            injF.style.margin = 0;
            injF.style.display = 'block';
            injF.style.cssFloat = 'none';
            injF.style.height = '254px';
            injF.style.overflow = 'hidden';
            injF.style.padding = 0;
            injF.style.width = '300px';
            injF.src = '/adm/ad/injectAd.iframe.html';

            if( b && ( !isTrellix || ( typeof isTrellix == "undefined" ) ) ) // All other tripod props
            {
                var cdiv = document.createElement('div');
                cdiv.style = "width:300px;margin:10px auto;";
                cdiv.appendChild( injF );
                b.insertBefore(cdiv, b.lastChild);
            } 
        }
  }( document.isTrellix ));
}

</script>

<div id="tb_container" style="background:#DFDCCF; border-bottom:1px solid #393939; position:relative; z-index:999999999!important">
<!--form name="search" onSubmit="return searchit()" id='header_search' >
<input type="text" placeholder="Search" size=30 name="search2" value="">
<input type="button" value="Go!" onClick="searchit()">
</form>
<style>
form#header_search {
    width: 916px;
    margin: 0 auto 8px;
    position: relative;
}


form#header_search input {
    height: 40px;
    font-size: 14px;
    line-height: 40px;
    padding: 0 8px;
    box-sizing: border-box;
    background: #F4F2E9;
    border: 1px solid #BBB8B8;
    transition: background-color 300ms ease-out,
                color 300ms ease;
}

form#header_search input[type="text"] {
    width: 100%;
}
form#header_search input[type="text"]:focus {
    border-color: #A2D054;
    background-color: #fff;
    box-shadow: 0 0px 12px -4px #A2D054;
}



form#header_search input[type="button"] {
    position: absolute;
    top: 1px;
    right: 1px;
    opacity: 1;
    background: #DFDCCF;
    color: #463734;
    width: 125px;
    cursor: pointer;
    height: 38px;
    border: none;
}
form#header_search input[type="text"]:focus ~ input[type='button']:hover,
form#header_search input[type='button']:hover {
    background-color: #A5CE56;
    color: #fff;
}
form#header_search input[type="text"]:focus ~ input[type='button'] {
    background-color: #52AEDF;
    color: #fff;
}

</style>

<script>
function searchit(){
    
    // determine environment 
    var search_env 
    if (lycos_ad_www_server.indexOf(".pd.") > -1) {
       search_env = 'http://search51.pd.lycos.com/a/';
    } else if (lycos_ad_www_server.indexOf(".qa.") > -1) {
       search_env = 'http://search51.qa.lycos.com/a/';
    } else {
       search_env = 'http://search51.lycos.com/a/';
    }

var search_term = encodeURIComponent(document.search.search2.value)
var search_url = search_env+search_term;
window.open(search_url);

return false
}
</script-->
<style>
    .adCenterClass{margin:0 auto}
</style>
<div id="tb_ad" class="adCenterClass" style="display:block!important; overflow:hidden; width:916px;">

<div id="ad_container" style="display:block!important; float:left; width:728px ">
<script type="text/javascript">
if (typeof lycos_ad !== "undefined" && "leaderboard" in lycos_ad) {
  document.write(lycos_ad['leaderboard']);
}
</script>
</div>
</div>
</div>
<script type="text/javascript">
if (typeof lycos_ad !== "undefined" && "slider" in lycos_ad) {
  document.write(lycos_ad['slider']);
}
</script> <!-- added 7/22 -->
<div id="FooterAd" style="background:#DFDCCF; border-top:1px solid #393939; clear:both; display:none; width:100%!important; position:relative; z-index:999999!important; height:90px!important"> 
<div class="adCenterClass" style="display:block!important; overflow:hidden; width:916px;">
<div id="footerAd_container" style="display:block!important; float:left; width:728px">
<iframe id="lycosFooterAdiFrame" style="border:0; display:block; float:left; height:96px; overflow:hidden; padding:0; width:750px"></iframe>
</div>
</div>
</div>