How to smooth data

Question

I have a list of the form dataTosmooth={{a,b,c},....} where a and b are coordinates and c is the data to be smoothed. In other words, smooth dataTosmooth[[All,3]] along dataTosmooth[[All,{1,2}]]. What I want is a GaussianFilter[] that can specify the spread of the smoothing in each coordinate direction (i believe this is the standard deviation of the smoothing kernel?).

My data is below:

dataTosmooth = {{-50.85000000000002`, 10.270358052733272`, 
35.71056426325409`}, {-41.10000000000002`, 2.873303230466569`, 
38.81568368585049`}, {-50.85000000000002`, 26.632846724285706`, 
32.673746341673144`}, {-41.10000000000002`, 19.236823144577595`, 
62.82335234608225`}, {-31.340000000000032`, 11.842619292783251`, 
68.53798691236852`}, {-21.590000000000032`, 4.449371441148591`, 
59.67967828331516`}, {-50.85000000000002`, 42.998118304091385`, 
24.63168690934504`}, {-41.10000000000002`, 35.60127021988911`, 
39.14245981028786`}, {-31.340000000000032`, 28.205878010311572`, 
108.66125712506734`}, {-21.590000000000032`, 20.813838889904257`, 
71.86692911207489`}, {-11.830000000000041`, 13.420766840507909`, 
56.90601725652569`}, {-2.07000000000005`, 6.025392936376173`, 
45.86143750472721`}, {-50.85000000000002`, 59.3621659426611`, 
15.762228586085156`}, {-41.10000000000002`, 51.96435329871178`, 
21.391649726002893`}, {-31.340000000000032`, 44.57034147474533`, 
93.0932476069022`}, {-21.590000000000032`, 37.178070307403786`, 
103.45958341304103`}, {-11.830000000000041`, 29.784020977809462`, 
71.78875677987466`}, {-2.07000000000005`, 22.389236995571`, 
56.71646586309835`}, {7.67999999999995`, 14.992388529677152`, 
47.14707785218505`}, {17.440000000000055`, 7.597788181370409`, 
46.556240183245045`}, {-50.85000000000002`, 75.72467877215065`, 
17.284429409153184`}, {-41.10000000000002`, 68.32743607405777`, 
41.167517535066395`}, {-31.340000000000032`, 60.932774236589516`, 
97.62585210895732`}, {-21.590000000000032`, 53.54074691792057`, 
100.79005357672948`}, {-11.830000000000041`, 46.14684985504994`, 
87.71485621033645`}, {-2.07000000000005`, 38.751590761310176`, 
61.202148655092174`}, {7.67999999999995`, 31.355932184885482`, 
53.28526015700777`}, {17.440000000000055`, 23.960184532899337`, 
51.37840013079427`}, {-41.10000000000002`, 84.69127060783131`, 
48.50554092059999`}, {-31.340000000000032`, 77.29765442653235`, 
96.52191875423944`}, {-21.590000000000032`, 69.90470174293358`, 
102.16980131134638`}, {-11.830000000000041`, 62.51153713633315`, 
87.28252975252263`}, {-2.07000000000005`, 55.1171707113319`, 
71.13287039055854`}, {7.67999999999995`, 47.719660637139974`, 
56.039176921150435`}, {17.440000000000055`, 40.32255868764509`, 
51.62321764477686`}, {-21.590000000000032`, 86.26760264399773`, 
99.89893442875152`}, {-11.830000000000041`, 78.87493853044776`, 
84.38244870824737`}, {-2.07000000000005`, 71.47982757170443`, 
66.47546126203261`}, {7.67999999999995`, 64.08276415269069`, 
56.678848788591324`}, {17.440000000000055`, 56.68762104179337`, 
49.11240169244424`}, {-2.07000000000005`, 87.84359593999416`, 
60.45632142299099`}, {7.67999999999995`, 80.44678282702743`, 
46.25808469878537`}, {17.440000000000055`, 73.05145942047734`, 
43.000967430977646`}, {17.440000000000055`, 89.41549423365234`, 
35.91954899494147`}, {-50.85000000000002`, 92.08824379203644`, 
8.605283260881098`}, {-50.85000000000002`, 108.45069667426264`, 
11.52966608362967`}, {-41.10000000000002`, 101.05393883219705`, 
44.11489034328432`}, {-31.340000000000032`, 93.66005797761179`, 
73.27571323433162`}, {-50.85000000000002`, 124.81532739053824`, 
13.822080107567034`}, {-41.10000000000002`, 117.41888025571974`, 
36.794739433783214`}, {-31.340000000000032`, 110.0246073374448`, 
71.61101451592485`}, {-21.590000000000032`, 102.6314654421303`, 
78.16186826068069`}, {-11.830000000000041`, 95.23887349513711`, 
74.51831620480968`}, {-50.85000000000002`, 141.18006853527996`, 
13.310659262410699`}, {-41.10000000000002`, 133.78046387959196`, 
57.95955788306187`}, {-31.340000000000032`, 126.38715905181873`, 
67.83749405749008`}, {-21.590000000000032`, 118.99470606408583`, 
60.94596541199428`}, {-11.830000000000041`, 111.60257187866787`, 
61.15398760506133`}, {-2.07000000000005`, 104.20728733201076`, 
48.67468541244001`}, {7.67999999999995`, 96.81027117502538`, 
45.52254935743384`}, {-50.85000000000002`, 157.54204574955395`, 
32.85902615720679`}, {-41.10000000000002`, 150.14434755173272`, 
58.74089291115688`}, {-31.340000000000032`, 142.75176035586526`, 
40.68660344634335`}, {-21.590000000000032`, 135.35972757157379`, 
43.96553536578396`}, {-11.830000000000041`, 127.96571938604754`, 
47.731975131980526`}, {-2.07000000000005`, 120.57125958422365`, 
46.88224024084176`}, {7.67999999999995`, 113.17334849523019`, 
33.146201139798805`}, {17.440000000000055`, 105.778455903297`, 
28.744622975436638`}, {-50.85000000000002`, 173.90647150665006`, 
13.951939506749587`}, {-41.10000000000002`, 166.50903777139433`, 
39.42513474929413`}, {-31.340000000000032`, 159.11491853678754`, 
36.678015213476314`}, {-21.590000000000032`, 151.72299087080495`, 
29.002943816102533`}, {-11.830000000000041`, 144.33048474012006`, 
45.740992555912044`}, {-2.07000000000005`, 136.93710041334336`, 
27.876090113213525`}, {7.67999999999995`, 129.53618856327074`, 
37.304938681091556`}, {17.440000000000055`, 122.14189062612374`, 
22.23726489476616`}, {-31.340000000000032`, 175.47796435907952`, 
52.748557326243535`}, {-21.590000000000032`, 168.08570710991364`, 
64.81976781815867`}, {-11.830000000000041`, 160.6931957243165`, 
44.599820627441986`}, {-2.07000000000005`, 153.2983792825559`, 
37.64146649640527`}, {7.67999999999995`, 145.9001470791707`, 
22.779087997547222`}, {17.440000000000055`, 138.504480760232`, 
18.657687959658883`}, {-11.830000000000041`, 177.05682588856274`, 
41.93606204688277`}, {-2.07000000000005`, 169.66138640423281`, 
45.416159018569594`}, {7.67999999999995`, 162.26467463897`, 
32.96873518957013`}, {17.440000000000055`, 154.8692135101764`, 
22.87621472184591`}, {7.67999999999995`, 178.62832066247012`, 
32.728904656282026`}, {17.440000000000055`, 171.23374350652944`, 
25.148891476564128`}, {-50.85000000000002`, 239.3621659426611`, 
12.480879376069625`}, {-41.10000000000002`, 231.96435329871179`, 
8.025642964896925`}, {-31.340000000000032`, 224.57034147474533`, 
33.438439706421754`}, {-21.590000000000032`, 217.1780703074038`, 
105.20882021009456`}, {-11.830000000000041`, 209.78402097780946`, 
46.7701363051253`}, {-2.07000000000005`, 202.389236995571`, 
48.438182769381434`}, {7.67999999999995`, 194.99238852967716`, 
36.58827851238699`}, {17.440000000000055`, 187.59778818137042`, 
29.716782076799635`}, {-50.85000000000002`, 255.72503363985203`, 
6.583537460970347`}, {-41.10000000000002`, 248.32777634141468`, 
11.033084337573124`}, {-31.340000000000032`, 240.93309418426773`, 
16.048551336491414`}, {-21.590000000000032`, 233.54104127754883`, 
73.47984281420318`}, {-11.830000000000041`, 226.1493860608138`, 
56.288509484618636`}, {-2.07000000000005`, 218.75216187654576`, 
38.96555155518782`}, {7.67999999999995`, 211.35655756554726`, 
34.24591847943343`}, {17.440000000000055`, 203.96085357284127`, 
29.93264438702334`}, {-41.10000000000002`, 264.6912706078313`, 
8.917437300031883`}, {-31.340000000000032`, 257.29765442653235`, 
22.77318159590351`}, {-21.590000000000032`, 249.90470174293358`, 
94.24297188650199`}, {-11.830000000000041`, 242.51186189307893`, 
66.90333885539648`}, {-2.07000000000005`, 235.1171707113319`, 
32.60697773483461`}, {7.67999999999995`, 227.71966063713998`, 
27.04036061150073`}, {17.440000000000055`, 220.32255868764508`, 
27.352197516835826`}, {-21.590000000000032`, 266.2683330630546`, 
87.00032327526148`}, {-11.830000000000041`, 258.87565693618865`, 
93.94211834954542`}, {-2.07000000000005`, 251.48052198668333`, 
24.320164473128056`}, {7.67999999999995`, 244.08342282394418`, 
22.173894786437497`}, {17.440000000000055`, 236.6882328805953`, 
25.82559735998376`}, {-2.07000000000005`, 267.843998447932`, 
24.36438969069408`}, {7.67999999999995`, 260.44714390335577`, 
24.329576907541977`}, {17.440000000000055`, 253.05180958679978`, 
21.350541234357504`}, {17.440000000000055`, 269.41549423365234`, 
22.553025074255565`}, {-50.85000000000002`, 190.26963741670468`, 
12.249710853730392`}, {-41.10000000000002`, 182.8723158359478`, 
19.09584681285435`}, {-50.85000000000002`, 206.6328467242857`, 
18.15002617078005`}, {-41.10000000000002`, 199.23682314457758`, 
22.89167058123981`}, {-31.340000000000032`, 191.84261929278324`, 
41.178883544846144`}, {-21.590000000000032`, 184.4493714411486`, 
95.6362818181468`}, {-50.85000000000002`, 222.99811830409138`, 
7.866947311378158`}, {-41.10000000000002`, 215.6012702198891`, 
8.608068017853943`}, {-31.340000000000032`, 208.20587801031158`, 
54.017223179278695`}, {-21.590000000000032`, 200.81383888990425`, 
84.16516084461551`}, {-11.830000000000041`, 193.4207668405079`, 
47.98167202172095`}, {-2.07000000000005`, 186.02539293637616`, 
46.21709910844685`}, {-50.85000000000002`, 272.0884633470491`, 
4.787857140725892`}, {-50.85000000000002`, 288.4525503585659`, 
10.812641790977825`}, {-41.10000000000002`, 281.0550168884835`, 
7.30768355910409`}, {-31.340000000000032`, 273.6608250905488`, 
40.51857351881985`}, {-50.85000000000002`, 304.81562802291336`, 
17.58421826525137`}, {-41.10000000000002`, 297.4192052801607`, 
12.388432104184938`}, {-31.340000000000032`, 290.02495126176467`, 
36.474884509755384`}, {-21.590000000000032`, 282.6318225761067`, 
68.86386570618869`}, {-11.830000000000041`, 275.2392380406287`, 
93.5971826499067`}, {-50.85000000000002`, 321.18006853527993`, 
8.22371841079204`}, {-41.10000000000002`, 313.78046387959193`, 
10.071113270140483`}, {-31.340000000000032`, 306.38715905181874`, 
16.99704533146858`}, {-21.590000000000032`, 298.99470606408585`, 
67.83629559461517`}, {-11.830000000000041`, 291.60257187866785`, 
125.48029964898875`}, {-2.07000000000005`, 284.20728733201076`, 
35.34755260976352`}, {7.67999999999995`, 276.8102711750254`, 
23.263237844289865`}, {-50.85000000000002`, 337.5423841647362`, 
11.36600510293745`}, {-41.10000000000002`, 330.146487811147`, 
18.917134746044393`}, {-31.340000000000032`, 322.75205173260684`, 
41.586135910901795`}, {-21.590000000000032`, 315.3597275715738`, 
92.72125969808648`}, {-11.830000000000041`, 307.9662966033093`, 
163.53064896220525`}, {-2.07000000000005`, 300.57157486151215`, 
40.001162639353375`}, {7.67999999999995`, 293.1740217393397`, 
21.27936243170834`}, {17.440000000000055`, 285.77880817562993`, 
20.515038910516356`}, {-50.85000000000002`, 353.90647150665006`, 
18.3776858173166`}, {-41.10000000000002`, 346.50903777139433`, 
27.376215041528297`}, {-31.340000000000032`, 339.1149185367875`, 
30.257997289972742`}, {-21.590000000000032`, 331.72299087080495`, 
99.86756530525814`}, {-11.830000000000041`, 324.3304847401201`, 
91.83169605316021`}, {-2.07000000000005`, 316.9371004133434`, 
18.836631864534585`}, {7.67999999999995`, 309.53618856327074`, 
19.95064660606268`}, {17.440000000000055`, 302.14189062612377`, 
16.002839201216762`}, {-31.340000000000032`, 355.4790590727488`, 
52.64555536795103`}, {-21.590000000000032`, 348.08678141464077`, 
67.83523568176052`}, {-11.830000000000041`, 340.69388671032993`, 
38.75331985778767`}, {-2.07000000000005`, 333.299033512983`, 
26.485557385110862`}, {7.67999999999995`, 325.90075350369267`, 
22.29703567741686`}, {17.440000000000055`, 318.50690611599794`, 
21.108851224071856`}, {-11.830000000000041`, 357.05682588856274`, 
46.125344443158355`}, {-2.07000000000005`, 349.6613864042328`, 
37.48141472783543`}, {7.67999999999995`, 342.26467463897`, 
31.004461775686405`}, {17.440000000000055`, 334.8692135101764`, 
26.973876250920995`}, {7.67999999999995`, 358.6283206624701`, 
42.92870834301914`}, {17.440000000000055`, 351.23374350652944`, 
40.47545552554042`}};

The noisy data looks like this:

The result I want looks somewhat like below.

This was generated using the squared exponential kernel in Predict[] as

sqExp = Predict[
   Thread[dataTosmooth[[All, {1, 2}]] -> dataTosmooth[[All, 3]]] , 
   Method -> {"GaussianProcess", 
     "CovarianceType" -> "SquaredExponential"}];
ContourPlot[
 sqExp[{x, y}], {x, -50, 17.5}, {y, 2.84, 358}, PlotRange -> Full, 
 PlotLegends -> 
  Placed[BarLegend[Automatic, LegendMargins -> {{0, 0}, {10, 5}}, 
    LegendLabel -> "contours", 
    LabelStyle -> {25, Italic, FontFamily -> "Times New Roman"}], 
   Below], Frame -> True, 
 FrameLabel -> {Style["x direction", 20, Italic], 
   Style["y direction, [\[Theta]]", 20, Italic]}, 
 LabelStyle -> {20, GrayLevel[0], FontFamily -> "Times New Roman"}, 
 LabelStyle -> {20, GrayLevel[0], FontFamily -> "Times New Roman"}, 
 ImageSize -> Large, GridLines -> Automatic
 ]

Answer 1

To apply e.g. a gaussian filter we need the data in an array. Toward this aim, we first sort the data;

d = Sort[dataTosmooth, First[#1] < First[#2] &]

Then we split the data according to the x values. This gives an array, from which we only take the third value (z or function value):

datz= Split[d = Sort[dat, First[#1] < First[#2] &], First[#1] === First[#2] &][[All, All, 3]]

These values can now be filtered. We can adjust the strength of the filter by: smthfac, I choose 5 for an example.:

smthfac = 5;
smth = GaussianFilter[datz, smthfac] ;

To draw a ContourPlot, we need to reassemble the data in the original format: {{x,y,z},..}:

datsmth=Transpose[Append[Transpose@d[[All, 1 ;; 2]], Flatten@smth]]

With this we can draw the plot:

ListContourPlot[datsmth]

For convenience, the code in compact form:

smthfac = 5;
smth = GaussianFilter[
   Split[d = Sort[dataTosmooth, First[#1] < First[#2] &], 
     First[#1] === First[#2] &][[All, All, 3]], smthfac] ;
ListContourPlot[
 Transpose[Append[Transpose@d[[All, 1 ;; 2]], Flatten@smth]]]

Answer 2

As I said in comment for Daniel's answer, for good smoothing you need more data: The original data:

 ListContourPlot[dataTosmooth]

It is impossible to improve it with any dances around.

Let's make the interpolation function and make the up-sampling to 201*201 matrix:

fun = Interpolation[dataTosmooth, InterpolationOrder -> 1];
{xmin, xmax} = MinMax[dataTosmooth[[All, 1]]];
{ymin, ymax} = MinMax[dataTosmooth[[All, 2]]];
newdata = 
  Table[fun[x, y], {y, ymin, ymax, (ymax - ymin)/200}, {x, xmin, 
    xmax, (xmax - xmin)/200}];

ListContourPlot[newdata[[4 ;; -4, 4 ;; -4]], InterpolationOrder -> 3]

As one can see, the result looks not much better. I've cropped the matrix for 4 lines at all sides to remove the artifacts of interpolation at the edges of x,y-domain.

This data is fully appropriate for smoothing with, let's say, GaussianFilter:

fd = GaussianFilter[newdata[[4 ;; -4, 4 ;; -4]], 10];
ListContourPlot[fd, InterpolationOrder -> 3]

Of course, you can choose the desired level of up-sampling and filtering.