Andrew ID: mkorada

Description of the project

The assignment involves gradient-domain processing techniques applied to tasks such as Poisson blending. The primary goal is to blend objects or textures from a source image into a target image seamlessly. This is achieved by setting up a problem that preserves the gradient of the source region while ignoring overall intensity. The project explores applications including blending, tone-mapping, and non-photorealistic rendering, with Poisson blending being the focus. The approach aims to maintain the perception of image gradients more than absolute intensities, facilitating smooth transitions between blended regions.

Toy problem

In the toy problem, you are tasked with reconstructing an image $v(x,y)$ from its gradients with respect to another image $s(x,y)$. We need to ensure that the gradients in the x and y directions of both images are similar. This is achieved by minimizing the squared differences of corresponding gradients in both x and y directions. Additionally, We enforce that the intensity at the top left corner of both images is the same to avoid ambiguity in intensity caused by the gradients. This problem is solved as a least squares optimization, which should allow you to recover the original image if done correctly. This exercise helps in understanding the gradient domain processing foundational to tasks like Poisson blending in image processing.

Poisson blending

Poisson blending is a technique in image processing where an object or texture from a source image is seamlessly blended into a target image. The method involves solving an optimization problem that aims to preserve the gradient of the source region within the blend. This approach emphasizes the importance of gradients over absolute intensity to achieve a natural look in the blended region, allowing for smooth transitions without noticeable seams between the source and target images. The result is a composite that appears coherent, as if the blended object naturally belongs in the scene.

Result (Good)

Result from the given images

Result (Bad)

Poisson blending might not work well in scenarios where the source and target images have very different lighting conditions or color palettes, as it can lead to mismatched seams or a noticeable outline around the blended object. It also struggles when there are complex textures or patterns that need to match up perfectly across the boundary of the blend. High levels of noise or artifacts in either the source or target images can also degrade the quality of the blend.