14/01/2026 3:01 PM - PACES
14/01/2026 3:01 PM
aLGuMq7FjZRnMtXHD-02_images_as_functions_PR.pdf
Problem
Finding and parameterizing boundaries in images.
Approach
Simultaneously smoothing the image and finding boundaries improves the boundary finding performance.
We have three competing objectives:
1. Make the smoothed image, f, similar to the original image, g.
2. Make the smoothed image, f, smooth (low gradient), everywhere that is not in the defined boundary, B.
3. Minimize the area that is defined as boundary, B.
A paired smoothed image/boundary pair that minimizes this energy will produce an image with large low variation sections separated by very high gradient sections marked as boundaries. Therefore, finding an optimization strategy that can minimize the energy will solve the boundary detection problem.
Contribution
This is a new way of solving the existing boundary finding problem. Their contribution is to propose the joint minimization of the image smoothing and boundary finding objectives.
Evaluation
They evaluate qualitatively through the proposal and description of examples. Their provide derivations that show how to solve their proposed minimization, but do not compare to other methods so the theoretical mathematics cannot be interpreted as evaluation.
Substantiation
Based on the evaluation, we cannot say that they substantiate an increase in performance from prior methods. However, they do substantiate that their method works in a constrained 1D case which can be fine for an entirely new proposed solution.