CS180: Project 2 - Fun with Filters and Frequencies!

When using the Derivative of Gaussian (DoG) filter:

1. We achieved the same results as the two-step process (Gaussian blur followed by gradient computation).
2. Q1.2: The edges appear smoother and more continuous compared to the simple gradient method.
3. Q1.2: The edges are very noisy in the previous finite differency operator without applying the Gaussian filter. It highlights the increase of intensity of pixels along x and y with the partial derivatives.
4. Q1.2: There is less apparent noise in the final edge detection result with the DoG filter.
5. Q1.2: We were able to achieve these results with fewer convolutions, making the process more computationally efficient. For the single convolution, the results are the same as before, except now the edges look a lot smoother than before and noise is a bit less apparent.

2.1 Image Sharpening

We use the Gaussian filter to sharpen images by enhancing high-frequency components. This technique involves subtracting a blurred version of the image from the original and then adding this high-frequency information back to the original image with varying intensities.

Taj Mahal Image Sharpening

We start with a sharp image (Taj Mahal) and apply different levels of sharpening to observe the effects.

San Francisco Street Image Sharpening

Next, we take a potentially blurry image of a San Francisco street and apply our sharpening technique.

New York Street Image Sharpening

Finally, we apply our sharpening technique to an image of a New York street.

Observations

1. Taj Mahal Image: As we increase the alpha value, we can see that the details in the image become more pronounced. The edges of the building and the textures in the sky become sharper. However, at higher alpha values (like 4), we start to see some artifacts and over-sharpening effects.

2. San Francisco and New York Street Images: For these images, we first applied a blur and then sharpened them. We can observe that:

• The blurred versions lose detail and appear softer.
• The sharpened versions (with alpha = 1) recover some of the lost detail and enhance edges, making the images appear clearer than the blurred versions.
• However, the sharpened versions may not fully recover all the details present in the original images, demonstrating the limitations of this technique when working with initially blurred images.

In conclusion, while image sharpening can enhance details and make images appear clearer, it's most effective when applied to images that are already reasonably sharp. When applied to blurred images, it can improve clarity but may not fully restore the original detail. Additionally, over-sharpening (using too high alpha values) can introduce unwanted artifacts and make the image appear unnatural.

2.2 Hybrid Images

We create hybrid images that appear differently when viewed up close versus from afar. The process involves combining high-frequency components of one image with low-frequency components of another.

Frequency Maps

To better understand how hybrid images work, we can visualize the frequency content of each image using Fourier transforms:

High and Low Pass Filters

To create the hybrid image, we apply a high-pass filter to the cat image and a low-pass filter to the dog image:

More fun examples

Let's explore more hybrid image examples using familiar faces!

Josh Hug and John Denero

Derek and Nutmeg

These additional examples further illustrate how hybrid images combine high-frequency details from one image with low-frequency components from another. The result is an image that appears different depending on viewing distance or image size.

The hybrid image is created by combining these filtered images. When viewed up close, the high-frequency details of the cat are more visible. From a distance, the low-frequency components of the dog dominate the perception.

2.3 Gaussian and Laplacian Stacks

In this section, we demonstrate the Gaussian and Laplacian stacks for both an apple and an orange image. These stacks are crucial for the multiresolution blending process.

Apple Gaussian Stack

Apple Laplacian Stack

Orange Gaussian Stack

Orange Laplacian Stack

These Gaussian and Laplacian stacks form the basis for our multiresolution blending process, which we'll explore in the next section.

2.4 Multiresolution Blending

In this section, we demonstrate the multiresolution blending process using the apple and orange images. We'll show the masked Laplacian layers and the final blended result.

Masked Laplacian Layers

Final Blended Result

The final blended image, often humorously referred to as the "Oraple", demonstrates the power of multiresolution blending. By combining the Laplacian stacks of the apple and orange images using a carefully crafted mask, we achieve a seamless transition between the two fruits. This technique allows us to create convincing composite images that smoothly blend different elements together.

Some more examples!

San Francisco Skyline and Space Blend (Irregular Mask)

This example demonstrates the use of an irregular mask to blend the San Francisco skyline with a space scene.

Sun and Moon Blend

The two drastically different textures and colors demonstrates the power of multiresolution blending.

Conclusion

This project has demonstrated how these processes can be used to enhance images, create intriguing visual effects, and seamlessly combine different visual elements.