I kind of understand how "filtering" works regarding different frequencies but I'm not sure I fully understand the notion of frequencies for the image...I remember we talked about why there's the white line along the x and y-axis direction...What does it represent?
simply_complicated
I also had the same question as above - what do frequencies really mean in the context of an image? Additionally, is there any spatial correspondence between the two images, i.e. do the locations of the frequencies translate to the spectrum on the right?
ryanmelon
Just want to check if my understanding of how to calculate the spectrum image is right. Say there's a point (x,y) in the spectrum. Then I calculate the directional derivatives on the direction y/x in the source image and express the value of it in the spectrum image. Is that right?
JimL
I found this article helpful for understanding Fourier transformation: https://plus.maths.org/content/fourier-transforms-images . We can think the image as a 2D point field (z=f(x,y), the z value is the grey scale of the image). The transformation is adding 2D sin functions (asin(ux+vy)) to "reconstruct" the point field, like what explained in slide 38. Also, the spectrum image is central symmetric because we are using the Euler's formula to express the sin functions.
supernova
I'm still confused about why the horizontal line in spectrum represent the horizontal outline in the origin.
KrystalTea
Are there any applications of such decomposition of images? I'm wondering in what way this is useful.
StickyBitz
Applying a low pass filter on an image is useful for certain image processing applications (Smooths out detail and reduces noise from poor camera quality), and though there's better methods to detect edges, the high-pass filter can also detect rapid changes in the image and produce a rough edge-detection map.
Gundam
@outousan The white lines here along x, y axis show that the man-made images(or images captured from man-made cameras) have more edges along x, y axis than other direction.
Zhuoqian
If we truncate frequencies with small magnitudes, we get an image compression algorithm.
heethesh
I think correlation and convolutions (in neural networks) can be computed more efficiently using Fast Fourier Transforms (FFT), where convolution simplifies to multiplication in frequency domain.
RyuK
@heethesh That's true.
jasonx
Imagine a 1D array of pixels. Each pixel has an associated intensity. If the intensity plot resembles a sine wave we can naturally associate a frequency with the image. Rapid intensity changes have high frequency while smooth intensity changes have low frequency. This can be extended to 2D. JPEG image compression makes use of decomposing an image into the sum of cosine waves over the frequency domain.
I kind of understand how "filtering" works regarding different frequencies but I'm not sure I fully understand the notion of frequencies for the image...I remember we talked about why there's the white line along the x and y-axis direction...What does it represent?
I also had the same question as above - what do frequencies really mean in the context of an image? Additionally, is there any spatial correspondence between the two images, i.e. do the locations of the frequencies translate to the spectrum on the right?
Just want to check if my understanding of how to calculate the spectrum image is right. Say there's a point (x,y) in the spectrum. Then I calculate the directional derivatives on the direction y/x in the source image and express the value of it in the spectrum image. Is that right?
I found this article helpful for understanding Fourier transformation: https://plus.maths.org/content/fourier-transforms-images . We can think the image as a 2D point field (z=f(x,y), the z value is the grey scale of the image). The transformation is adding 2D sin functions (asin(ux+vy)) to "reconstruct" the point field, like what explained in slide 38. Also, the spectrum image is central symmetric because we are using the Euler's formula to express the sin functions.
I'm still confused about why the horizontal line in spectrum represent the horizontal outline in the origin.
Are there any applications of such decomposition of images? I'm wondering in what way this is useful.
Applying a low pass filter on an image is useful for certain image processing applications (Smooths out detail and reduces noise from poor camera quality), and though there's better methods to detect edges, the high-pass filter can also detect rapid changes in the image and produce a rough edge-detection map.
@outousan The white lines here along x, y axis show that the man-made images(or images captured from man-made cameras) have more edges along x, y axis than other direction.
If we truncate frequencies with small magnitudes, we get an image compression algorithm.
I think correlation and convolutions (in neural networks) can be computed more efficiently using Fast Fourier Transforms (FFT), where convolution simplifies to multiplication in frequency domain.
@heethesh That's true.
Imagine a 1D array of pixels. Each pixel has an associated intensity. If the intensity plot resembles a sine wave we can naturally associate a frequency with the image. Rapid intensity changes have high frequency while smooth intensity changes have low frequency. This can be extended to 2D. JPEG image compression makes use of decomposing an image into the sum of cosine waves over the frequency domain.