[2021] Learning to Solve Hard Minimal Problems

[gatheluck]

論文リンク

• arXiv

公開日（yyyy/mm/dd）

2021/12/06

概要

Research Question

研究で明らかにしたい問を端的に表したもの.

Elevator Pitch

[潜在的なニーズを満たしたり、潜在的な課題を解決したり] したい [対象ユーザー] 向けの, [提案手法] という手法は, [提案手法のカテゴリー] です. これは [提案手法の出来ること] ができ, [代替手段のSoTA] とは違って, [差別化の決定的な特徴] が備わっている.

TeX

% yyyy/mm/dd
@article{
    hruby2023learning,
    title={Learning to Solve Hard Minimal Problems},
    author={Petr Hruby and Timothy Duff and Anton Leykin and Tomas Pajdla},
    journal=arXiv # "2112.03424",
    year={2023}
}

---

Links

• 第１１回全日本コンピュータビジョン勉強会
• cvpaper.challenge

[gatheluck]

• An denotes a set of anchors covering n% of the training datasets.
• B1, An: 理想状態
• B2, An: selects the starting problem as the nearest anchor to the target problem
• B3, An: selects the starting problem as the nearest anchor to the target problem measured by the Mahalanobis distance
• MLP+T, An: is our method selecting the starting problem as the one from An with the highest score given by the MLP

ita_{t}: mean effective solving time (average time to obtain one correct solution)

[gatheluck]

To demonstrate our method on a hard problem, we develop an efficient solver for the “Scranton” minimal problem obtained by relaxing the overconstrained problem of four points in three views (4pt) [50].

We train a model that predicts a starting problem for a single path real HC method to find a good solution.

Our solver is implemented efficiently in C++ and evaluated on the state-of-the-art data in computer vision.

It successfully solves about 26.3% of inputs in 16.3µs, Tab. 4.

In Sec. 9 we show that when used in RANSAC, about 4 samples suffice on average to obtain a valid candidate of camera geometry in 61.6µs.

No such efficient solver has been known for this problem before.

The best-known runtime for a very carefully designed approximation of the problem, reported in [50], was on the order of milliseconds.

We thus achieve more than ten times speedup compared to [50]. -> 10~100倍の高速化

[gatheluck]

カメラ姿勢推定のような、多くの偽の解をもつ連立方程式を解く必要があるタスクがμsオーダーで解けるようになった。

• カメラ姿勢推定は3D CV分野で頻出の重要なタスクの１つ。
• 従来はサンプリングによって推定されたカメラ姿勢から最も良いものを選択していた（RANSAC）。
• 提案手法はサンプリング後、分類器を使って解が既知の問題から近いもの（アンカー）を選び出し、アンカーを始点として問題を解くことで偽の解を弾いている。