At first, I was confused about how to connect an image or shape with the concept of frequencies. The way I ended up understanding it is to view the triangle as a function. And the reason why sharp edges mean high frequencies is that the value of the function changes really drastically and steeply at the edges. In contrast, blurry edges mean the frequencies change less slowly.
BohanYu
Another way I found useful (also mentioned in the lecture) to understand "frequency" in this case is to view it as a change in color. The edge of the triangle has very high frequency because the color suddenly change from pure red to pure white. To remove such "high frequencies", we blur the edges so that the color gradually changes from pure red to pure white, instead of a sudden change.
ashvindhawan
Thanks @bohan and @linda for the help understanding this. Question -- is it possible to create a sample with intermediate values without removing high frequencies first? For example, if the original image contained some amount of blur at the edges, would this create the same sample we see on the right, or is what I just described the same thing as antialiasing?
At first, I was confused about how to connect an image or shape with the concept of frequencies. The way I ended up understanding it is to view the triangle as a function. And the reason why sharp edges mean high frequencies is that the value of the function changes really drastically and steeply at the edges. In contrast, blurry edges mean the frequencies change less slowly.
Another way I found useful (also mentioned in the lecture) to understand "frequency" in this case is to view it as a change in color. The edge of the triangle has very high frequency because the color suddenly change from pure red to pure white. To remove such "high frequencies", we blur the edges so that the color gradually changes from pure red to pure white, instead of a sudden change.
Thanks @bohan and @linda for the help understanding this. Question -- is it possible to create a sample with intermediate values without removing high frequencies first? For example, if the original image contained some amount of blur at the edges, would this create the same sample we see on the right, or is what I just described the same thing as antialiasing?