Bones are the support of the body. They are composed of many inorganic compounds and other organic materials that all together can be used to determine the mineral density of the bones. The bone mineral density is a measure index that is widely used as an indicator of the health of the bone. A typical manner to evaluate the quality of the bone is a densitometry study; a dual x-ray absorptiometry system based study that has been widely used to assess the mineral density of some animals’ bones. However, despite the success stories of utilizing these systems in many different applications, it is a very expensive method that requires frequent calibration processes to work properly. Moreover, its usage in small species applications (e.g., rodents) has not been quite demonstrated yet. Following this argument, it is suggested that there is a need for an instrument that would perform such a task in a more reliable and economical manner. Therefore, in this paper we explore the possibility to develop a new, affordable, and reliable single x-ray absorptiometry system. The method consists of utilizing a single x-ray source, an x-ray image sensor, and a computer platform that all together, as a whole, will allow us to calculate the mineral density of the bone. Utilizing an x-ray transmission theory modified through a version of the Lambert-Beer law equation, a law that expresses the relationship among the energy absorbed, the thickness, and the absorption coefficient of the sample at the x-rays wavelength to calculate the mineral density of the bone can be advantageous. Having determined the parameter equation that defines the ratio of the pixels in radiographies and the bone mineral density [measured in mass per unit of area (g/cm²)], we demonstrated the utility of our novel methodology by calculating the mineral density of Wistar rats’ femur bones.

A study of a class of openings and closings is investigated using reconstruction criteria. The main goal in studying these transformations consists of eliminating some inconveniences of the morphological opening (closing) and the opening (closing) by reconstruction. The idea in building these new openings and closings comes from the notions of filters by reconstruction and levelings. In particular, concerning the notion of levelings, a study of a class of lower and upper levelings is carried out. The original work of levelings is due to Meyer, who proposes this notion and introduces some criteria to build the levelings in the general case (extended levelings and self-dual transformations). We see the criteria proposed by Meyer as reconstruction criteria during the reconstruction process from a marker image into the reference image. We show that new openings and closings are obtained, enabling intermediate results between the traditional opening (closing) and the opening (closing) by reconstruction. Some applications are studied to validate these transformations. © 2005 SPIE and IS&T.