Abstract:
In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We pre...Show MoreMetadata
Abstract:
In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields.
Published in: IEEE Transactions on Image Processing ( Volume: 18, Issue: 6, June 2009)
CREATIS, INSA, UCB, CNRS/UMR, Villeurbanne, France
Olivier Bernard received the B.S. and Ph.D. degrees in electrical engineering in 2003 and 2006, respectively, from the National Institute for Applied Sciences of Lyon (INSA-Lyon), France.
In 2007, he was a Postdoctoral Research Fellow at the Biomedical Imaging Group of the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. He is now an Associate Professor at INSA-Lyon and a member of the CREATIS-LRMN laboratory ...Show More
Olivier Bernard received the B.S. and Ph.D. degrees in electrical engineering in 2003 and 2006, respectively, from the National Institute for Applied Sciences of Lyon (INSA-Lyon), France.
In 2007, he was a Postdoctoral Research Fellow at the Biomedical Imaging Group of the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. He is now an Associate Professor at INSA-Lyon and a member of the CREATIS-LRMN laboratory ...View more
CREATIS, INSA, UCB, CNRS/UMR, Villeurbanne, France
Denis Friboulet (M'06) was born in Bordeaux, France, in 1961. He received the engineering degree (electrical engineering) in 1984 and the Ph.D. degree (biomedical engineering) in 1990, both from the National Institute for Applied Sciences of Lyon, INSA-Lyon, France.
He is currently a Professor with NSA-Lyon and a member of the CREATIS-LRMN laboratory (CNRS 5220, INSERM U630, INSA-Lyon, Claude Bernard Lyon I University of L...Show More
Denis Friboulet (M'06) was born in Bordeaux, France, in 1961. He received the engineering degree (electrical engineering) in 1984 and the Ph.D. degree (biomedical engineering) in 1990, both from the National Institute for Applied Sciences of Lyon, INSA-Lyon, France.
He is currently a Professor with NSA-Lyon and a member of the CREATIS-LRMN laboratory (CNRS 5220, INSERM U630, INSA-Lyon, Claude Bernard Lyon I University of L...View more
Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Philippe Thévenaz was born in 1962 in Lausanne, Switzerland. He graduated in January 1986 from the École polytechnique fédérale de Lausanne (EPFL), Switzerland, with a diploma in microengineering, and received the Ph.D. degree in June 1993 with a thesis on the use of the linear prediction residue for text-independent speaker recognition.
He joined the Institute of Microtechnology (IMT) of the University of Neuchâtel, Switz...Show More
Philippe Thévenaz was born in 1962 in Lausanne, Switzerland. He graduated in January 1986 from the École polytechnique fédérale de Lausanne (EPFL), Switzerland, with a diploma in microengineering, and received the Ph.D. degree in June 1993 with a thesis on the use of the linear prediction residue for text-independent speaker recognition.
He joined the Institute of Microtechnology (IMT) of the University of Neuchâtel, Switz...View more
Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Michael Unser (M'89–SM'94–F'99) received the M.S. (summa cum laude) and Ph.D. degrees in electrical engineering in 1981 and 1984, respectively, from the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland.
From 1985 to 1997, he was a Scientist with the National Institutes of Health, Bethesda, MD. He is now full Professor and Director of the Biomedical Imaging Group, EPFL. His main research area is biomedical image...Show More
Michael Unser (M'89–SM'94–F'99) received the M.S. (summa cum laude) and Ph.D. degrees in electrical engineering in 1981 and 1984, respectively, from the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland.
From 1985 to 1997, he was a Scientist with the National Institutes of Health, Bethesda, MD. He is now full Professor and Director of the Biomedical Imaging Group, EPFL. His main research area is biomedical image...View more
Contents CREATIS, INSA, UCB, CNRS/UMR, Villeurbanne, France
Olivier Bernard received the B.S. and Ph.D. degrees in electrical engineering in 2003 and 2006, respectively, from the National Institute for Applied Sciences of Lyon (INSA-Lyon), France.
In 2007, he was a Postdoctoral Research Fellow at the Biomedical Imaging Group of the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. He is now an Associate Professor at INSA-Lyon and a member of the CREATIS-LRMN laboratory (CNRS 5220, INSERM U630, INSA-Lyon, Claude Bernard Lyon I University of Lyon). His main research area is medical image processing. He has a strong interest in image segmentation, statistical modeling, and sampling theories.
Olivier Bernard received the B.S. and Ph.D. degrees in electrical engineering in 2003 and 2006, respectively, from the National Institute for Applied Sciences of Lyon (INSA-Lyon), France.
In 2007, he was a Postdoctoral Research Fellow at the Biomedical Imaging Group of the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. He is now an Associate Professor at INSA-Lyon and a member of the CREATIS-LRMN laboratory (CNRS 5220, INSERM U630, INSA-Lyon, Claude Bernard Lyon I University of Lyon). His main research area is medical image processing. He has a strong interest in image segmentation, statistical modeling, and sampling theories.View more
CREATIS, INSA, UCB, CNRS/UMR, Villeurbanne, France
Denis Friboulet (M'06) was born in Bordeaux, France, in 1961. He received the engineering degree (electrical engineering) in 1984 and the Ph.D. degree (biomedical engineering) in 1990, both from the National Institute for Applied Sciences of Lyon, INSA-Lyon, France.
He is currently a Professor with NSA-Lyon and a member of the CREATIS-LRMN laboratory (CNRS 5220, INSERM U630, INSA-Lyon, Claude Bernard Lyon I University of Lyon). His research interests include signal processing (spectral analysis, statistical modeling) and image processing (statistics-based deformable models, level-set based segmentation, motion estimation and analysis), applied in the field of echocardiographic imaging.
Denis Friboulet (M'06) was born in Bordeaux, France, in 1961. He received the engineering degree (electrical engineering) in 1984 and the Ph.D. degree (biomedical engineering) in 1990, both from the National Institute for Applied Sciences of Lyon, INSA-Lyon, France.
He is currently a Professor with NSA-Lyon and a member of the CREATIS-LRMN laboratory (CNRS 5220, INSERM U630, INSA-Lyon, Claude Bernard Lyon I University of Lyon). His research interests include signal processing (spectral analysis, statistical modeling) and image processing (statistics-based deformable models, level-set based segmentation, motion estimation and analysis), applied in the field of echocardiographic imaging.View more
Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Philippe Thévenaz was born in 1962 in Lausanne, Switzerland. He graduated in January 1986 from the École polytechnique fédérale de Lausanne (EPFL), Switzerland, with a diploma in microengineering, and received the Ph.D. degree in June 1993 with a thesis on the use of the linear prediction residue for text-independent speaker recognition.
He joined the Institute of Microtechnology (IMT) of the University of Neuchâtel, Switzerland, where he worked in the domain of image processing (optical flow) and in the domain of speech processing (speech coding and speaker recognition). He was a Visiting Fellow with the Biomedical Engineering and Instrumentation Program, National Institutes of Health (NIH), Bethesda MD, where he developed research interests that include splines and multiresolution signal representations, geometric image transformations, and biomedical image registration. Since 1998, he has been a senior researcher with the EPFL.
Philippe Thévenaz was born in 1962 in Lausanne, Switzerland. He graduated in January 1986 from the École polytechnique fédérale de Lausanne (EPFL), Switzerland, with a diploma in microengineering, and received the Ph.D. degree in June 1993 with a thesis on the use of the linear prediction residue for text-independent speaker recognition.
He joined the Institute of Microtechnology (IMT) of the University of Neuchâtel, Switzerland, where he worked in the domain of image processing (optical flow) and in the domain of speech processing (speech coding and speaker recognition). He was a Visiting Fellow with the Biomedical Engineering and Instrumentation Program, National Institutes of Health (NIH), Bethesda MD, where he developed research interests that include splines and multiresolution signal representations, geometric image transformations, and biomedical image registration. Since 1998, he has been a senior researcher with the EPFL.View more
Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Michael Unser (M'89–SM'94–F'99) received the M.S. (summa cum laude) and Ph.D. degrees in electrical engineering in 1981 and 1984, respectively, from the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland.
From 1985 to 1997, he was a Scientist with the National Institutes of Health, Bethesda, MD. He is now full Professor and Director of the Biomedical Imaging Group, EPFL. His main research area is biomedical image processing. He has a strong interest in sampling theories, multiresolution algorithms, wavelets, and the use of splines for image processing. He has published over 150 journal papers on those topics and is one of ISI's Highly Cited authors in Engineering (http://isihighlycited.com).
Dr. Unser has held the position of associate Editor-in-Chief (2003–2005) for the IEEE Transactions on Medical Imaging and has served as Associate Editor for the same journal (1999–2002; 2006–2007), the IEEE Transactions on Image Processing (1992–1995), and the IEEE Signal Processing Letters (1994–1998). He is currently member of the editorial boards of Foundations and Trends in Signal Processing, the SIAM Journal of Imaging Sciences, and Sampling Theory in Signal and Image Processing. He co-organized the first IEEE International Symposium on Biomedical Imaging (ISBI2002). He was the founding chair of the technical committee of the IEEE-SP Society on Bio Imaging and Signal Processing (BISP). He received the 1995 and 2003 Best Paper Awards and the 2000 Magazine Award from the IEEE Signal Processing Society.
Michael Unser (M'89–SM'94–F'99) received the M.S. (summa cum laude) and Ph.D. degrees in electrical engineering in 1981 and 1984, respectively, from the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland.
From 1985 to 1997, he was a Scientist with the National Institutes of Health, Bethesda, MD. He is now full Professor and Director of the Biomedical Imaging Group, EPFL. His main research area is biomedical image processing. He has a strong interest in sampling theories, multiresolution algorithms, wavelets, and the use of splines for image processing. He has published over 150 journal papers on those topics and is one of ISI's Highly Cited authors in Engineering (http://isihighlycited.com).
Dr. Unser has held the position of associate Editor-in-Chief (2003–2005) for the IEEE Transactions on Medical Imaging and has served as Associate Editor for the same journal (1999–2002; 2006–2007), the IEEE Transactions on Image Processing (1992–1995), and the IEEE Signal Processing Letters (1994–1998). He is currently member of the editorial boards of Foundations and Trends in Signal Processing, the SIAM Journal of Imaging Sciences, and Sampling Theory in Signal and Image Processing. He co-organized the first IEEE International Symposium on Biomedical Imaging (ISBI2002). He was the founding chair of the technical committee of the IEEE-SP Society on Bio Imaging and Signal Processing (BISP). He received the 1995 and 2003 Best Paper Awards and the 2000 Magazine Award from the IEEE Signal Processing Society.View more
