Signal Processing 88 (2008) 1125–1133 Review Morphological multiscale fingerprints from connected transformations Edgar A. Rivas-Araiza, Jorge D. Mendiola-Santiban˜ez à , Gilberto Herrera-Ruiz Doctorado en Ingenierı´a, Universidad Auto´noma de Quere´taro, Cerro de las Campanas, CP. 76010, Quere´taro, Me´xico Received 5 June 2006; received in revised form 19 June 2007; accepted 19 November 2007 Available online 4 December 2007 Abstract In this paper a multiscale study based on the use of morphological connected transformations is presented. In particular, the morphological opening and closing by reconstruction are used as connected transformations. These transformations have the characteristic of preserving contours without introducing new information, in addition to smoothing the processed image as the size of the structuring element increases. Due to this, both connected filters and the identity are used as primitives to introduce two operators that allow a multiscale treatment to the processed image in accordance with the scale parameter. The multiscale morphological operators are called opening–closing by reconstruction and closing–opening by reconstruction, respectively. In the case of the opening–closing by reconstruction transformation, the propagation of extrema when the structuring element enlarges has an interesting behavior. In addition, the fingerprints of the image given as a function of regional maxima, regional minima and scale parameter are defined. Finally, the proposals of this work are illustrated with some examples. r 2007 Elsevier B.V. All rights reserved. Keywords: Scale space; Fingerprints; Multiscale morphology; Connected operators Contents 1. Introduction ..................................................................... 1126 2. Definitions and background .......................................................... 1127 2.1. Reconstruction transformations and connectivity ...................................... 1127 3. Scale space from the opening–closing by reconstruction ...................................... 1128 3.1. Multiscale opening–closing by reconstruction ........................................ 1128 3.2. Fingerprints from connected transformations ........................................ 1129 4. Conclusions ..................................................................... 1132 References ...................................................................... 1132 ARTICLE IN PRESS www.elsevier.com/locate/sigpro 0165-1684/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2007.11.019 à Corresponding author. Tel.: +52 442 1921200x6023; fax: +52 442 1921200. E-mail addresses: erivas@uaq.mx (E.A. Rivas-Araiza), mendijor@uaq.mx (J.D. Mendiola-Santiban˜ez), gherrera@uaq.mx (G. Herrera-Ruiz).