Symmetrical Cubic Bézier Curves Refinement

I'm looking for an expert in computer vision and curve analysis to help develop a process that refines polylines into symmetrical cubic Bézier curves.

Key tasks:
- Identify geometric shapes from polylines
- Explore reflective symmetry within these shapes
- Complete the curves to form smooth transitions

Deliverables will include a well-structured algorithm and accompanying visualization tools. Experience with graphic design and engineering CAD applications will be beneficial, as the primary use of these Bézier curves will be in the realm of computer vision.

The polylines we will be working with typically represent geometric shapes, so a strong understanding and ability to work with these types of shapes is crucial. I need someone who can help identify the shapes and refine them into symmetrical cubic Bézier curves.

The most important aspect of symmetry we will be focusing on is reflective symmetry. This will be key in the curve refinement process, so proficiency in recognizing and applying this type of symmetry will be beneficial. Please include relevant experience and examples of similar work in your proposal.