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MeanFilter

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

MeanFilter[image, r] averages over a (2r+1) x (2r+1) neighbourhood. This IS a convolution with a normalised box, and it is implemented as one rather than as a separate averaging loop -- two implementations of one identity is how the identity quietly stops holding. Being a full rectangle the kernel is separable, so it costs kw + kh rather than kw * kh.

Examples (46)

Every input below was run against the current Mathilda build and its output recorded.

Basic Examples (5)

In[1]:= ImageData[MeanFilter[Image[{{0., 0., 0.}, {0., 1., 0.}, {0., 0., 0.}}], 1]]
Out[1]= {{0.111111, 0.111111, 0.111111}, {0.111111, 0.111111, 0.111111}, {0.111111, 0.111111, 0.111111}}

In[2]:= chk = Image[Table[If[Mod[Quotient[i - 1, 2] + Quotient[j - 1, 2], 2] == 0, 0., 1.], {i, 1, 16}, {j, 1, 16}], "Real"];

In[3]:= MeanFilter[chk, 2]
Out[3]= -Image-

In[4]:= ImageDimensions[MeanFilter[chk, 2]]
Out[4]= {16, 16}

In[5]:= ImageType[MeanFilter[chk, 1]]
Out[5]= "Real"

Scope (22)

In[6]:= chk = Image[Table[If[Mod[Quotient[i - 1, 2] + Quotient[j - 1, 2], 2] == 0, 0., 1.], {i, 1, 16}, {j, 1, 16}], "Real"];

In[7]:= disk = Image[Table[N[Boole[(i - 8.5)^2 + (j - 8.5)^2 <= 25]], {i, 1, 16}, {j, 1, 16}], "Real"];

In[8]:= ramp = Image[Table[N[(j - 1)/15], {i, 1, 16}, {j, 1, 16}], "Real"];

In[9]:= zone = Image[Table[N[(1 + Cos[((i - 16)^2 + (j - 16)^2)/40.])/2], {i, 1, 32}, {j, 1, 32}], "Real"];

In[10]:= noise = Image[Table[N[Mod[i*37 + j*17, 101]]/101, {i, 1, 32}, {j, 1, 32}], "Real"];

In[11]:= rgb = Image[Table[{N[i/16], N[j/16], 0.5}, {i, 1, 16}, {j, 1, 16}], "Real"];

In[12]:= sky = Image[Table[{N[0.15 + 0.7 (16 - i)/16], N[0.35 + 0.45 (16 - i)/16], N[0.85 - 0.35 (16 - i)/16]}, {i, 1, 16}, {j, 1, 24}], "Real"];

In[13]:= bit = Image[Table[Boole[Mod[i + j, 2] == 0], {i, 1, 8}, {j, 1, 8}]];

In[14]:= byte = Image[Table[Mod[i*13 + j*7, 256], {i, 1, 16}, {j, 1, 16}]];

In[15]:= vol = Image3D[Table[N[Mod[z*7 + y*13 + x*3, 97]]/97, {z, 1, 8}, {y, 1, 10}, {x, 1, 12}], "Real"];

In[16]:= MeanFilter[disk, 1]
Out[16]= -Image-

In[17]:= MeanFilter[ramp, 2]
Out[17]= -Image-

In[18]:= MeanFilter[zone, 2]
Out[18]= -Image-

In[19]:= MeanFilter[noise, 3]
Out[19]= -Image-

In[20]:= MeanFilter[rgb, 1]
Out[20]= -Image-

In[21]:= MeanFilter[sky, 2]
Out[21]= -Image-

In[22]:= MeanFilter[bit, 1]
Out[22]= -Image-

In[23]:= MeanFilter[byte, 2]
Out[23]= -Image-

In[24]:= MeanFilter[vol, 1]
Out[24]= -Image-

In[25]:= ImageChannels[MeanFilter[rgb, 2]]
Out[25]= 3

In[26]:= ImageDimensions[MeanFilter[vol, 1]]
Out[26]= {12, 10, 8}

In[27]:= MeanFilter[chk, 4]
Out[27]= -Image-

Applications (6)

In[28]:= zone = Image[Table[N[(1 + Cos[((i - 16)^2 + (j - 16)^2)/40.])/2], {i, 1, 32}, {j, 1, 32}], "Real"];

In[29]:= noise = Image[Table[N[Mod[i*37 + j*17, 101]]/101, {i, 1, 32}, {j, 1, 32}], "Real"];

In[30]:= rgb = Image[Table[{N[i/16], N[j/16], 0.5}, {i, 1, 16}, {j, 1, 16}], "Real"];

In[31]:= Binarize[MeanFilter[noise, 2]]
Out[31]= -Image-

In[32]:= EdgeDetect[MeanFilter[zone, 2]]
Out[32]= -Image-

In[33]:= ImageDimensions[MeanFilter[Import[Export["/tmp/mathilda_ex.png", rgb]], 2]]
Out[33]= {16, 16}

Properties & Relations (10)

In[34]:= chk = Image[Table[If[Mod[Quotient[i - 1, 2] + Quotient[j - 1, 2], 2] == 0, 0., 1.], {i, 1, 16}, {j, 1, 16}], "Real"];

In[35]:= ramp = Image[Table[N[(j - 1)/15], {i, 1, 16}, {j, 1, 16}], "Real"];

In[36]:= rgb = Image[Table[{N[i/16], N[j/16], 0.5}, {i, 1, 16}, {j, 1, 16}], "Real"];

In[37]:= vol = Image3D[Table[N[Mod[z*7 + y*13 + x*3, 97]]/97, {z, 1, 8}, {y, 1, 10}, {x, 1, 12}], "Real"];

In[38]:= ImageDimensions[MeanFilter[chk, 3]] === ImageDimensions[chk]
Out[38]= True

In[39]:= ImageChannels[MeanFilter[rgb, 2]] === ImageChannels[rgb]
Out[39]= True

In[40]:= ImageData[MeanFilter[ramp, 0]] === ImageData[ramp]
Out[40]= True

In[41]:= Max[Flatten[ImageData[MeanFilter[chk, 2]]]] <= 1.0
Out[41]= True

In[42]:= Min[Flatten[ImageData[MeanFilter[chk, 2]]]] >= 0.0
Out[42]= True

In[43]:= ImageDimensions[MeanFilter[vol, 2]] === ImageDimensions[vol]
Out[43]= True

Neat Examples (3)

In[44]:= zone = Image[Table[N[(1 + Cos[((i - 16)^2 + (j - 16)^2)/40.])/2], {i, 1, 32}, {j, 1, 32}], "Real"];

In[45]:= MeanFilter[zone, 4]
Out[45]= -Image-

In[46]:= MeanFilter[zone, 1]
Out[46]= -Image-

Implementation notes

Attributes: Protected.

References

See also: Image3D