B-Spline Eğri Uydurmada Optimum Serbest Düğüm Noktalarının Seçilmesi için Guguk Kuşu Arama Algoritması

Yıl 2018, Cilt: 2 Sayı: 2, 120 - 127, 10.11.2018

İsmail Koç , Özkan İnik

https://doi.org/10.30516/bilgesci.375269

Öz

Genellikle eğriyi
yeniden oluşturmak olarak bilinen eğrilere veri noktaları uydurma, bilgisayar
destekli tasarım / imalat alanında (CAD / CAM) önemli bir problemdir. 3D lazer
tarama ile elde edilen genellikle yüksek boyutlu ve gürültülü bir diziden oluşan
veri noktalarının serbest forma sahip bir parametrik eğriye (tipik olarak bir
B-spline) uydurulması gereken tersine mühendislik alanında bu problemle
sıklıkla karşılaşılmaktadır. Bu problemin üstesinden gelebilmek için çok sayıda
yöntem mevcut olmasına rağmen, şu ana kadar problemin tatmin edici genel bir
çözümü elde edilebilmiş değildir. Bu çalışmada, eğri uydurma problemini çözmek
için, doğadaki diğer evcil kuşların yuvalarına yumurtalarını bırakan guguk
kuşlarından esinlenilerek geliştirilmiş optimizasyon yöntemlerinden biri olan
Guguk kuşu arama algoritması (CS) kullanılmıştır. Veri noktalarından eğri elde
etmek için ise tersine mühendislik kullanılmıştır. Ayrıca, düğüm yerleri ve
düğüm sayısı eğri tahmininde serbest bırakılmış olup, CS yöntemi ile bu parametreler
arama uzayında rastgele seçilmiştir. Bu şekilde en küçük hata oranına sahip
eğri tahmininin elde edilmesi amaçlanmıştır. Deneysel çalışmalarda eğri uydurma
için, literatürde sıklıkla kullanılan beş farklı fonksiyon tercih edilmiştir.
Deneysel sonuçlarda, her bir fonksiyon için orijinal eğri ve tahmin edilen eğri
karşılaştırmalı olarak sunulmuş olup, elde edilen sonuçlar çoğu fonksiyon için
CS yöntemi ile tahmin edilen eğrilerin orijinal eğrilere çok benzer sonuçlar
ürettiğini göstermiştir.

Anahtar Kelimeler

B-spline Eğri Uydurma, Guguk kuşu Arama algoritması (CS), Serbest düğüm yerleştirme, Optimizasyon

Cuckoo Search Algorithm for Optimal Choice of Free Knots in B-spline Data Fitting

Öz

Fitting data points to curves
commonly known as curve reconstruction a significant problem in computer aided
design/manufacturing (CAD/CAM). This problem is frequently encountered in the
field of reverse engineering where a free-form parametric curve (typically a
B-spline) with a set of (usually a high-dimensional and noisy) data points,
obtained by 3D laser scanning, has to be fitted. Although there are a number of
methods to come up with this problem, until now there has not been a
satisfactory general solution to the problem. In this study, the cuckoo search
algorithm (CS), one of the optimization methods inspired by a bird species
named cuckoo that leave their eggs in the nest of other host birds, is used to
solve the problem of curve fitting. Reverse engineering is used to obtain the
curve from the data points. In addition, the knot positions and number of knot
are free variables of the problem in the estimation of the curve, and these
parameters are randomly selected in the search space by the CS method. In this
way, the curve estimate with the smallest error rate is aimed to obtain in this
study. Five different functions frequently used in the literature for curve
fitting are preferred in the experimental studies. In the experimental results,
the original curve and the predicted curve for each function are presented
comparatively, and the results obtained show that for most functions, the
curves predicted by the CS method produce very similar results to the original
curve.

Anahtar Kelimeler

B-spline Curve Fitting, Cuckoo Search algorithm (CS), Free knot placement, Optimization

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