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D. Lee, T. Pavlidis, "OneDimensional Regularization with Discontinuities," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 6, pp. 822829, November, 1988.  
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@article{ 10.1109/34.9105, author = {D. Lee and T. Pavlidis}, title = {OneDimensional Regularization with Discontinuities}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {10}, number = {6}, issn = {01628828}, year = {1988}, pages = {822829}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.9105}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  OneDimensional Regularization with Discontinuities IS  6 SN  01628828 SP822 EP829 EPD  822829 A1  D. Lee, A1  T. Pavlidis, PY  1988 KW  edge analysis; 1D regularization; computerized picture processing; cubic splines; discontinuities; discrete regularization; data points; computerised picture processing; splines (mathematics) VL  10 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Regularization is equivalent to fitting smoothing splines to the data so that efficient and reliable numerical algorithms exist for finding solutions. however, the results exhibit poor performance along edges and boundaries. To cope with such anomalies, a more general class of smoothing splines that preserve corners and discontinuities is studied. Cubic splines are investigated in detail, since they are easy to implement and produce smooth curves near all data points except those marked as discontinuities or creases. A discrete regularization method is introduced to locate corners and discontinuities in the data points before the continuous regularization is applied.
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