TY - GEN
T1 - Comparison and evaluation of first derivatives estimation
AU - Bustacara-Medina, César
AU - Flórez-Valencia, Leonardo
N1 - Publisher Copyright:
© Springer International Publishing AG 2016.
PY - 2016
Y1 - 2016
N2 - Computing derivatives from observed integral data is known as an ill-posed inverse problem. The ill-posed qualifier refers to the noise amplification that can occur in the numerical solution if appropriate measures are not taken (small errors for measurement values on specified points may induce large errors in the derivatives). For example, the accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution, affecting the accuracy of segmentation methods. In our case, we want to obtain an upper air-ways segmentation, so it is necessary to compute the first derivatives as accurately as possible, in order to use gradient-based segmentation techniques. For this reason, the aim of this paper is to present a comparative analysis of several methods (finite differences, interpolation, operators and regularization), that have been developed for numerical differentiation. Numerical results are presented for artificial and real data sets.
AB - Computing derivatives from observed integral data is known as an ill-posed inverse problem. The ill-posed qualifier refers to the noise amplification that can occur in the numerical solution if appropriate measures are not taken (small errors for measurement values on specified points may induce large errors in the derivatives). For example, the accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution, affecting the accuracy of segmentation methods. In our case, we want to obtain an upper air-ways segmentation, so it is necessary to compute the first derivatives as accurately as possible, in order to use gradient-based segmentation techniques. For this reason, the aim of this paper is to present a comparative analysis of several methods (finite differences, interpolation, operators and regularization), that have been developed for numerical differentiation. Numerical results are presented for artificial and real data sets.
UR - http://www.scopus.com/inward/record.url?scp=84989869710&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-46418-3_11
DO - 10.1007/978-3-319-46418-3_11
M3 - Conference contribution
AN - SCOPUS:84989869710
SN - 9783319464176
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 121
EP - 133
BT - Computer Vision and Graphics - International Conference, ICCVG 2016, Proceedings
A2 - Datta, Amitava
A2 - Wojciechowski, Konrad
A2 - Chmielewski, Leszek J.
A2 - Kozera, Ryszard
PB - Springer Verlag
T2 - International Conference on Computer Vision and Graphics, ICCVG 2016
Y2 - 19 September 2016 through 21 September 2016
ER -