Prove What You Build.
Not What You Claim.

### 🚀 Feature Description Improve the observability, diagnostics, and basic safety of the kornia-algebra::optim module by exposing richer optimization results, clearer termination information, and optional validation utilities. The goal is to make the optimizer easier to trust, debug, and integrate into real-world vision and geometry pipelines, without changing the underlying optimization algorithms. ### 📂 Feature Category Geometry ### 💡 Motivation The optim module introduced in PR #664 provides a solid functional foundation, but it currently behaves largely as a black box. Users have limited visibility into why an optimization converged, stalled, or failed, and little support for validating custom factors or Jacobians. This makes debugging difficult, slows experimentation, and reduces confidence when integrating the optimizer into larger systems such as SLAM, bundle adjustment, or pose refinement pipelines. Improving observability and safety would significantly lower the barrier to adoption and complement ongoing benchmarking efforts. ### 💭 Proposed Solution Introduce a set of usability- and safety-focused improvements, including: - Extend OptimizerResult to expose useful diagnostics such as: - Cost history across iterations - Final gradient norm - More informative termination details - Optional per-iteration metadata (e.g. step accepted/rejected) - Improve termination reporting to clearly distinguish convergence, divergence, numerical instability, and limit-based stops. - Add an opt-in finite-difference Jacobian validation utility to help users debug custom factors. - Enforce basic safety guards where applicable (e.g. automatic quaternion normalization during SE(3) optimization). These changes focus on API design and diagnostics rather than modifying solver mathematics or performance characteristics. ### 📚 Library Reference This proposal is inspired by practices used in established optimization and geometry libraries such as: - C

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# 🐞 Issue Report / Feature Request Thank you for taking the time to open an issue! Please fill out the details below to help us understand and resolve it efficiently. --- ## 📌 Issue Type Please select one: - [ ] Bug report 🐞 - [ ] Feature request 🚀 - [x] UI/UX improvement 🎨 - [ ] Documentation update 📚 - [ ] Other --- ## 📝 Description The summarizer currently returns output in **Markdown (`.md`) format**, but the extension displays it as **raw text** instead of rendering it properly. This results in visible markdown syntax (such as `#`, `**`, `-`) rather than formatted headings, bold text, and lists. This issue aims to **parse and render markdown output correctly** in the UI. --- ## 🔁 Steps to Reproduce (for bugs) 1. Open any blog or documentation page 2. Click the extension icon 3. Generate a summary (any summary type) 4. Observe that the summary output shows raw markdown syntax --- ## ✅ Expected Behavior - Markdown output should be **properly parsed and rendered** in the UI - Headings, bullet points, bold/italic text should display correctly - The summary should look clean and readable --- ## ❌ Actual Behavior - Markdown syntax is displayed as plain text - Headings, lists, and formatting are not rendered --- ## 🖼️ Screenshots (if applicable) <img width="1821" height="830" alt="Image" src="https://github.com/user-attachments/assets/61a4f459-9c11-4cb6-b48b-6523ace4bf82" /> --- ## 🧪 Environment Details - Chrome Version: Latest - OS: Windows / macOS / Linux - Extension Version: 1.0.0 --- ## 💡 Additional Context Suggested approaches: - Use a lightweight markdown parser (e.g., `marked`) - Or implement a basic custom markdown-to-HTML parser - Ensure rendered HTML is safely sanitized This is a **good first issue** and suitable for beginners. --- ### 🙌 Are you willing to work on this issue? - [ ] Yes - [x] No