({{, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image] 
shows the squared magnitude of the discrete Fourier transform (power spectrum) of image.}, {, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n]
shows the average of power spectra of non-overlapping partitions of size n×n.}, {, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n,d]
uses partitions with offset d.}, {, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n,d,wfun]
applies a smoothing window wfun to each partition.}, {, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n,d,wfun,m]
pads partitions with zeros to length m prior to the computation of the transform.}})

OpenersNotesSection(Spacer1)Details and Options

(RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram]) logarithmically scales the power spectrum of the image and adjusts the values so that they range from 0 to 1.

In (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n,d,wfun], the smoothing window wfun can be specified using a window function that will be sampled between -1/2 and 1/2, or a list of length n. The default window is (RefLink[DirichletWindow, paclet:ref/DirichletWindow]), which effectively does no smoothing.

(RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n] is equivalent to (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,n,n,(RefLink[DirichletWindow, paclet:ref/DirichletWindow]),n].

(RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,{(Subscript[n, 1]),(Subscript[n, 2])}] partitions image into blocks of size (Subscript[n, 1])×(Subscript[n, 2]).

For 3D images, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram])[image,{(Subscript[n, 1]),(Subscript[n, 2]),(Subscript[n, 3])}] partitions image into blocks of size (Subscript[n, 1])×(Subscript[n, 2])×(Subscript[n, 3]).

For multichannel images, (RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram]) returns a multichannel image where each channel is the power spectrum computed for each channel separately.

(RefLink[ImagePeriodogram, paclet:ref/ImagePeriodogram]) accepts the (RefLink[Alignment, paclet:ref/Alignment]) option that determines the location of the zero frequency term. The default is (RefLink[Alignment, paclet:ref/Alignment])->(RefLink[Center, paclet:ref/Center]). With (RefLink[Alignment, paclet:ref/Alignment])->{(RefLink[Left, paclet:ref/Left]),(RefLink[Top, paclet:ref/Top])}, the zero frequency term is placed at the top-left corner of the image.

OpenersPrimaryExamplesSection(Spacer1)Examples  (6)

OpenersExampleSection0(Spacer1)Basic Examples  (3)

Power spectrum of an image of a disk:

ImagePeriodogram[]

Power spectrum of a color image:

ImagePeriodogram[]

Power spectrum of a 3D image of the hydrogen wave function:

Image3D[ImagePeriodogram[],ColorFunction->"GrayLevelOpacity"]

OpenersExampleSection1(Spacer1)Options  (1)

OpenersExampleSubsection0(Spacer1)Alignment  (1)

By default, the power spectrum is centered:

ImagePeriodogram[]

Use (RefLink[Alignment, paclet:ref/Alignment])->{(RefLink[Left, paclet:ref/Left]),(RefLink[Top, paclet:ref/Top])} to avoid centering:

ImagePeriodogram[,Alignment->{Left,Top}]

Centering can be switched off for one dimension:

ImagePeriodogram[,Alignment->{Left,Center}]

OpenersExampleSection2(Spacer1)Properties & Relations  (2)

Create the image periodogram from the power spectrum data:

s=PeriodogramArray[];
ImageAdjust[Image[Log10[s]]]

Use (RefLink[PeriodogramArray, paclet:ref/PeriodogramArray]) to change the default visualization settings of the image power spectrum:

s=PeriodogramArray[];
ArrayPlot[Log[s],ColorFunction->"Rainbow",ColorFunctionScaling->True]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[PeriodogramArray, paclet:ref/PeriodogramArray])  ▪  (RefLink[Periodogram, paclet:ref/Periodogram])  ▪  (RefLink[Fourier, paclet:ref/Fourier])  ▪  (RefLink[SpectrogramArray, paclet:ref/SpectrogramArray])  ▪  (RefLink[Spectrogram, paclet:ref/Spectrogram])  ▪  (RefLink[DirichletWindow, paclet:ref/DirichletWindow])  ▪  (RefLink[Partition, paclet:ref/Partition])  ▪  (RefLink[ImagePartition, paclet:ref/ImagePartition])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Feature Detection, paclet:guide/FeatureDetection])}, {▪(RefLinkPlain[Signal Processing, paclet:guide/SignalProcessing])}, {▪(RefLinkPlain[Computer Vision, paclet:guide/ComputerVision])}, {▪(RefLinkPlain[Fourier Analysis, paclet:guide/FourierAnalysis])}, {▪(RefLinkPlain[Summation Transforms, paclet:guide/SummationTransforms])}})}})