Eulerian motion modulation
In one embodiment, a method of amplifying temporal variation in at least two images includes converting two or more images to a transform representation. The method further includes, for each spatial position within the two or more images, examining a plurality of coefficient values. The method additionally includes calculating a first vector based on the plurality of coefficient values. The first vector can represent change from a first image to a second image of the at least two images describing deformation. The method also includes modifying the first vector to create a second vector. The method further includes calculating a second plurality of coefficients based on the second vector.
1. A method of amplifying temporal variation in at least two images, the method comprising:
for each particular pixel of the at least two images, detecting a temporal variation of the particular pixel of the at least two images by applying a bandpass filter configured to analyze frequencies over time, the resulting detected temporal variation of the particular pixel between the two images being below a particular threshold; and
amplifying the detected temporal variation of each particular pixel; and
providing at least two modulated images by adding the amplified temporal variation to the at least two images by synthesizing the modulated images, for an amplification factor α, according to ƒ(x+(1+α)δ(t)), δ(t) being a displacement function.
2. The method of claim 1 , wherein detecting the temporal variation employs temporal processing.
3. The method of claim 1 , wherein detecting the temporal variation employs spatial processing, the spatial processing removing noise.
4. A system for amplifying temporal variation in at least two images, the system comprising:
a pixel examination module configured to, for each particular pixel of the at least two images, detect a temporal variation of the particular pixel of the at least two images by applying a bandpass filter configured to analyze frequencies over time, the resulting detected temporal variation of the particular pixel between the two images being below a particular threshold; and
a signal processing module configured to:
amplify the detected temporal variation of each particular pixel, and
provide at least two modulated images by adding the amplified temporal variation to the at least two images by synthesizing the modulated images, for an amplification factor α, according to ƒ(x+(1+α)δ(t)), δ(t)being a displacement function.
5. The system of claim 4 , wherein the pixel examination module is further configured to detect temporal variation by employing temporal processing.
6. The system of claim 4 , wherein the pixel examination module is further configured to employ spatial processing, the spatial processing removing noise.
7. The method of claim 1 , wherein applying the bandpass filter further includes, for each pixel value, analyzing a one-dimensional (1D) image intensity profile.
8. The method of claim 7 , wherein the 1D image intensity profile is based on a function ƒ(x+δ(t)), where δ(t) is a displacement function.
9. The system of claim 4 , wherein the pixel examination module is further configured to, for each pixel value, analyzing a one-dimensional (1D) image intensity profile.
10. The system of claim 9 , wherein the 1D image intensity profile is based on a function ƒ(x+δ(t)), where δ(t) is a displacement function.