World of Mathematics for Gale Group- myassignmenthelp.com

Question: Discuss about theWorld of Mathematics for Gale Group. Answer: Geometric Transformation of Images The geometric transformation of images is based on the modification of spatial relationships which do exist between the pixels in an image and has turned to out to be a key element in the post processing of images. The geometric transformation at time lead to the change in the appearances of the images and also the content of the images (Foley, Dam, Feiner and Hughes, 1990). In other words, the geometric transformation is simply related to the image processing techniques which will be able to transform the image, known as the source into a transformed image known as the destination. The transformation is simply the terms which is used to describe the manipulation of the shapes and images in four different ways of an image which include the point, line of shape. In the transformation, the original shape of the object is referred to as pre-image and the final shape and position is the image (Pratt, 2001). There are different types of transformation of images which include the translati ons, reflections, rotations, magnifications and dilations among others. The transformation is able to reposition the points, lines or shapes of the images of any dimensions (Goshtasby, 2005). The nature of this image processing tool is that it helps to map each of the pre-image to an image point. It helps the viewers to have different perspectives of the different images and able to derive different knowledge on them. Changing the aspects helps viewers to see other details which are not seen from the original position of point of the pre-image. This is able to lead to different perspectives and knowledge on the images which have been transformed. There are different significances and implications which are derived from the use of the geometric transformation of images. First, the geometric image transformation is used to remove any distortion which the images to have. The changes on the lines, points and shapes of the images do happen in most cases in order to correct distortion which may have happened on the images (Pratt, 2001). This helps to make the images finer and clearer for the viewers to be able t derive different points from the images. The distortion may be hindering different perspectives of the images and therefore key to ensure that the viewers seen what is needed. The geometric transformation will enhance these views of the key aspects and therefore their application will enhance this point (Karam and Rice, 2000). Each change and geometric transformation is able to change the images on desired shape and point, which will enhance the viewers to have different perspective when they look at the images. The geometr ical distortions are able to interfere with the shape and the information which are needed in the images. The use of geometric transformation is able to lead to the removal of such errors which might have happened on the images. In addition, the use of the geometric transformation of images is used as an image registration. The image registration is key in different areas which involve the medical sector, computer visions ad the automatic recognition of the target images. It helps to analyze the details of the images in depth and therefore able to make the viewers to see different perspectives of the images. It helps in the comparison of the data on different images and therefore enhancing the different viewers when the images are analyzed (Karam and Rice, 2000). In addition, this aspect is able to help in the recognition of any errors when the analysis and comparison factors of the images. The use of the geometric transformation of the images therefore enhances the view of inner details from the different perspectives. This ensures that the different details which are needed can be derived from the respective images. Therefore, the implication of the use of the geometric transformation is able to enhance th e view of key details which are needed by different people (Gonzalez and Woods, 2002). This means that the aspect will be used to ensure that the images can be viewed in certain angles which will be able to lead to the viewing of the required details (Narins, 2001). Moreover, the geometric transformation of images is used to enhance and create special effects of images. The transformation of the images can lead to different images from a single perspectives and therefore enhancing different details and views. The camera orientations at sometimes may be not perfect and the use of geometric transformation is used to correct such errors which may result from the camera orientation. The use of the transformation enhances the viewing of the image from the key orientation which the users need them (Karam and Rice, 2000). It enhances the changes of the position and angle at which the image can be viewed and therefore enhancing the different tastes and preferences of the viewers. The orientation is able to bring out the required information which the viewer need from the particular orientation which they want to view the images. The transformation of the images enhance the effects of the viewers gaining the different aspects of the images through the various orientation angles. In terms of the linear algebraic and mathematical techniques, the geometric transformation of images is able to apply the different aspects and formulae of the matrix sector. The finding of the Eigen values and vectors is enhanced through the spatial transformation which is used to map one point to another. This is able to enhance the solving of the different aspects of the matrices (Gonzalez and Woods, 2002). Moreover, the use of linear solutions of the transformation is achieved through the formation of equations from the transformations such as the magnifications, rotations, translations and shear. These aspects are able to solve different linear solutions of equilibrium equations and this is solved through the use of the geometric transformation of images (Narins, 2001). In addition, these methods are used in the interpolation in order to calculate new points. This helps to come up with solutions of the changes which happen on the objects leading to the formation of various equat ions and solving them. The forward and inverse transformations are solved through the geometric transformation of the images. This helps to solve the inverses of the matrices. References FOLEY, J.D., DAM, A., FEINER, S.K., AND HUGHES, J.F. (1990). Computer Graphics: Principles and Practice, 2nd edition, Addison-Wesley Publishing Company. GONZALEZ, R.C., AND WOODS, M.P. (2002). Digital image processing. Prentice Hall, 2nd edition. GOSHTASBY A. (2005). 2-D and 3-D Image Registration for Medical, Remote Sensing, and Industrial Applications, Wiley Press. KARAM, L.J., AND RICE, D. (2000). Teaching image processing to high-school students. Signal Processing Education Workshop. NARINS, B. (2001). ed. World of Mathematics, Detroit: Gale Group. PRATT, W.K. (2001). Digital image processing. John Willey and Sons, Inc., 3rd edition, 2001.