Blue Book

Hola les dejo el link para bajar gratuito el Blue Book (Proceedings of the Michigan Morphometrics Workshop) en formato PDF. Si bien es un poco antiguo, (1990) tiene algunos conceptos básicos de morfometría y discusiones muy interesante sobre la relación entre morfología y filogenia. http://deepblue.lib.umich.edu/handle/2027.42/49535. En esta URL hay también muchos otros trabajos que pueden bajarse de forma gratuita.

Morfometría en artefactos líticos

Morfometría geométrica en artefactos líticos:
Hola. Mi trabajo se centra en la aplicación de técnicas del estudio de la forma de intrumentos líticos arqueológicos. Estos métodos tienen gran potencial en arqueología ya que permiten describir la forma de una manera cuantitativa, no tipológica. Por ejemplo el empleo de la función thin plate splines aplicada en un conjunto de puntas de proyectil (puntas de flecha y de dardo) sirve para explorar las zonas de la morfología más sensibles a cambios relacionados con el uso de los intrumentos así como a los requerimientos de performance de los mismos.


Para este análisis utilicé el programa Past (http://folk.uio.no/ohammer/past/download.html) En donde las partes de la morfología que se expanden aparecen en verde y las que se contraen en lila. Aquí se observa que algunas partes de la punta de poryectil están más sujetas a expansión y otras a contracción, relacionada con el proceso de continuo reavivamiento de los filos. Las partes que se expanden se relacionan con la variabilidad existente en el punto en que las puntas de proyectil eran fijadas a un mango. El programa Past es de distribción gratuita y realiza también otros análisis morfométricos como Fourier elíptico y Eigenshape analysis. Puede leer directamente cordenadas tomadas mediante el programa tps dig de James Rohlf.
También es posible con este programa realizar análisis de componentes principales a partir de la función thin plate spline (relative warp analysis) o componentes principales sobre coordenadas alineadas mediante el método de procrustes. Los primeros ejes de variación pueden ser luego utilizados en distintos análisis entre variación morfológica y otras variables métricas o información ambiental, espacial o cronológica.

Literatura reciente, 1

Slice, D.E. 2007.Geometric Morphometrics. Annual Review of Anthropology 36: 261-281.
(Volume publication date September 2007)
ABSTRACT. Morphometrics, the field of biological shape analysis, has undergone major change in recent years. Most of this change has been due to the development and adoption of methods to analyze the Cartesian coordinates of anatomical landmarks. These geometric morphometric (GM) methods focus on the retention of geometric information throughout a study and provide efficient, statistically powerful analyses that can readily relate abstract, multivariate results to the physical structure of the original specimens. Physical anthropology has played a central role in both the development and the early adoption of these methods, just as it has done in the realm of general statistics, where it has served as a major motivating and contributing force behind much innovation. This review surveys the current state of GM, the role of anthropologists in its development, recent applications of GM in physical anthropology, and GM-based methods newly introduced to, or by, anthropology, which are likely to impact future research.

Acronyms and Definitions

Bending energy: minimized in the construction of thin-plate splines; measures the bendedness or kinkiness of the interpolated space between landmarks

Geometric morphometrics (GM): morphometric methods, often based on Cartesian coordinates of landmarks, that retain all geometric information in the data throughout an analysis

GPA: generalized Procrustes analysis

Morphometrics: examines central tendencies of shape, shape variation, group differences in shape, and associations of shape with extrinsic factors

PCA: principal components analysis

Procrustes analysis: the analysis of shape coordinates generated by the least-squares superimposition of configurations of landmarks

Shape: geometric properties of an object invariant to position, orientation, and isometric (global magnification/reduction) size differences

Shape variable: geometric variables invariant to position, orientation, and isometric size. Superimposed landmark coordinates are shape variables. Raw coordinates are not

Thin-plate spline: a visualization tool based on the interpolation of landmark differences mapping one set of landmark locations exactly onto another

La "forma" adquiere forma

Bookstein FL. 1996. Biometrics, biomathematics and the morphometric synthesis. Bull. Math. Biol. 58(2):313–65 [CrossRef] [ISI]

(1)	University of Michigan, 300 North Ingalls Building, 48109-2007 Ann Arbor, MI, USA

Received: 16 July 1995

Abstract At the core of contemporarymorphometrics—the quantitative study of biological shape variation—is a synthesis of two originally divergent methodological styles. One contributory tradition is the multivariate analysis of covariance matrices originally developed as biometrics and now dominant across a broad expanse of applied statistics. This approach, couched solely in the linear geometry of covariance structures, ignores biomathematical aspects of the original measurements. The other tributary emphasizes the direct visualization of changes in biological form. However, making objective the biological meaning of the features seen in those diagrams was always problematical; also, the representation of variation, as distinct from pairwise difference, proved infeasible.

To combine these two variants of biomathematical modeling into a valid praxis for quantitative studies of biological shape was a goal earnestly sought though most of this century. That goal was finally achieved in the 1980s when techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry and computer graphics were combined in a coherent new system of tools for the complete regionalized quantitative analysis oflandmark points together with the biomedical images in which they are seen.

In this morphometric synthesis, correspondence of landmarks (biologically labeled geometric points, like “bridge of the nose”) across specimens is taken as a biomathematical primitive. The shapes of configurations of landmarks are defined as equivalence classes with respect to the Euclidean similarity group and then represented as single points in David Kendall'sshape space, a Riemannian manifold with Procrustes distance as metric. All conventional multivariate strategies carry over to the study of shape variation and covariation when shapes are interpreted in the tangent space to the shape manifold at an average shape. For biomathematical interpretation of such analyses, one needs a basis for the tangent space compatible with the reality of local biotheoretical processes and explanations at many different geometric scales, and one needs graphics for visualizing average shape differences and other statistical contrasts there. Both of these needs are managed by thethin-plate spline, a deformation function that has an unusually helpful linear algebra. The spline also links the biometrics of landmarks to deformation analysis of the images from which the landmarks originally arose.

This article reviews the history and principal tools of this synthesis in their biomathematical and biometrical context and demonstrates their usefulness in a study of focal neuroanatomical anomalies in schizophrenia.

Contornos sin marcas pero con semi-marcas

Buscando referencias actualizadas para el curso encontré la siguiente (aunque sin pdf):

Fred L. Bookstein. 1997. Landmark methods for forms without landmarks: morphometrics of group differences in outline shape. Medical Image Analysis Volume 1, Issue 3, April 1997, Pages 225-243. Available online 10 April 2002.

Abstract. Morphometrics, a new branch of statistics, combines tools from geometry, computer graphics and biometrics in techniques for the multivariate analysis of biological shape variation. Although medical image analysts typically prefer to represent scenes by way of curving outlines or surfaces, the most recent developments in this associated statistical methodology have emphasized the domain of landmark data: size and shape of configurations of discrete, named points in two or three dimensions. This paper introduces a combination of Procrustes analysis and thin-plate splines, the two most powerful tools of landmark-based morphometrics, for multivariate analysis of curving outlines in samples of biomedical images. The thin-plate spline is used to assign point-to-point correspondences, called semi-landmarks, between curves of similar but variable shape, while the standard algorithm for Procrustes shape averages and shape coordinates is altered to accord with the ways in which semi-landmarks formally differ from more traditional landmark loci. Subsequent multivariate statistics and visualization proceed mainly as in the landmark-based methods. The combination provides a range of complementary filters, from high pass to low pass, for effects on outline shape in grouped studies. The low-pass version is based on the spectrum of the spline, the high pass, on a familiar special case of Procrustes analysis. This hybrid method is demonstrated in a comparison of the shape of the corpus callosum from mid-sagittal sections of MRI of 25 human brains, 12 normal and 13 with schizophrenia.

Keywords: morphometrics; multivariate analysis; outlines; Procrustes analysis; thin-plate spline