Project 2

Part 1: Fun with Filters

Part 1.1: Finite Difference Operator

The gradient is a vector consisting of partial derivatives, we calculate the magnitude by taking square root of the sum of the squared x partial derivative and squared y partial derivative. (since this is 2 dimension)

While a clear edge image could be shown, there are many gaps between the edge.

Part 1.2: Derivative of Gaussian (DoG) Filter

We could see that the edge is a lot smoother in the gradient image. As a result, the edge image performs better (less gap in between) with curated threshold. Also, we recognize that the edge image generated from blurring the original then convolve is identical to the edge image genereated by convolve the gaussian kernel then convolve, proving that convolution has same property as multiply.

Part 2: Fun with Frequencies!

Part 2.1: Image "Sharpening"

Compare the original and the sharpened images, we could see that the fine details of each car is strengthened in sharpened images, those include the grill, vague shadow of branches on glass,and small area reflection of protrude parts.

When sharpen the sharped already image of BMW i7, we could see that during the blur step (Sharped i7 without high freq) , the image resembles the original image. After the second sharpen is applied, it seems like all the strokes on the car has been amplified, making it seem unreal.

Part 2.2: Hybrid Images

From the fourier transform above, we could see that the the filtered high freq input is got strengthened for its non-vertial and non-horizontal frequencies, those are the detail on nutmeg's face, the filtered low freq input is reduced to mostly horizontal and vertical, constructing the basic structure of the hybrid image. The final hybrid image is just as we could predict from the fourier analysis: the fine detail of nutmeg's face, its mustache and facial hair is prominant when looked closely, and the underlying structure of Derek's face could be seen from afar.

This is the hybrid picture of two cars: ferrari laferrari and mclaren p1, I assume this is a successful example as looking close we could see the high freq input clearly (the ferrari) and barely sees the low freq input, and vice versa when look from afar. I think this good hybrid is due to I chose two cars with similar structure (both are sport cars) and they are of similar color (black glass, red-ish/black paint).

This is the hybrid picture of two emojis: eyeroll and tears of joy, I assume this is a failed example as both of the high and low frequencies are present no matter obversed from what distance. I think this is due to the big structural difference between the two emojis, while the background is a big yellow circle, their eyes and mouth vary vastly in color, shape and angle. The edges are also very abrupt in those two emojis, making both emoji present even with filtering.

Part 2.3: Gaussian and Laplacian Stacks

Part 2.4: Multiresolution Blending

The car blending worked well. However, I couldn't find a way to do smooth mask for the ciruclar mask, hence the hand_nose blending looks pretty bad with the circular seam at the middle.

Conclusion

From this project, we could see that multiresolution blending is quite a strong tool, the final output image is almost flawless. The laplacian stack is good at hybriding two images, which could be resonablely infered that it could be used to mix sounds. When detecting gradients, applying a gaussian filter could significantly reduce the noise in final output. Oversharpening an image does not make it clear, but makes it look unreal instead.