Model Selection for Geometric Fitting: Geometric Ale and Geometric MDL

Contrasting "geometric fitting", for which the noise level is taken as the asymptotic variable, with "statistical inference", for which the number of observations is taken as the asymptotic variable, we give a new definition of the "geometric AIC" and the "geometric MDL" as the counterparts of Akaike's AIC and Rissanen's MDL. We discuss various theoretical and practical problems that emerge from our analysis. Finally, we show, doing experiments using synthetic and real images, that the geometric MDL does not necessarily outperform the geometric AIC and that the two criteria have very different characteristics

Uncertainty modeling and model selection for geometric inference

We first investigate the meaning of &#34;statistical methods&#34; for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to &#34;geometric fitting&#34; and &#34;geometric model selection&#34; and point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. Then, we derive the &#34;geometric AIC&#34; and the &#34;geometric MDL&#34; as counterparts of Akaike's AIC and Rissanen's MDL. We show by experiments that the two criteria have contrasting characteristics in detecting degeneracy. </p

Uncertainty Modeling and Geometric Inference

We investigate the meaning of "statistical methods" for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to "geometric fitting" and "geometric model selection", We point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. We also compare the capability of the "geometric AIC" and the "geometric MDL' in detecting degeneracy. Next, we review recent progress in geometric fitting techniques for linear constraints, describing the "FNS method", the "HEIV method", the "renormalization method", and other related techniques. Finally, we discuss the "Neyman-Scott problem" and "semiparametric models" in relation to geometric inference. We conclude that applications of statistical methods requires careful considerations about the nature of the problem in question

Growth State Map for Automatic Harvesting of Tomato Fruits

九州工業大学博士学位論文 学位記番号：生工博甲第406号 学位授与年月日：令和3年3月25日1. 序論|2. 栽培領域のモザイク画像の生成|3. トマト果実の検出及び生育状態の推定|4. 収穫しやすさの評価|5. 生育状態マップの導入|6. 結論九州工業大学令和2年