Active contours

Active contours Active contours are one category of variational methods that have been used widely within image segmentation applications. An energy functional is defined with arguments as the image parameters and a closed curve that partitions the objects in the image. There are two main methods of representing the curves such as (a) extrinsic and (b) intrinsic. Extrinsic representation keeps function values at boundary points. Intrinsic lets use of functions that are defined on all the point of the image and are more desirable. Intrinsic representation of a planar curve C using an auxiliary function is denoted as C = f(x; y) j (x; y) = 0g (22) where (x; y) is called level set function of curve C and the zero level of (x; y) is taken as the contour. Curvature  of the closed curve C with level set function  is given by  = div( 5 k5k ) (23) The deformation of the contour is reprsented in a numerical form as a partial differential equation @(x;y) @t =j 5(x; y) j ( + ((x; y))) (24) where  is a constant speed term to push or pull the contour. Mean curvature of the level set function is defined as: ((x; y)) = xx2 yà ´Ã‚€Â€Â€2xyxy+yy2 x (2 x+2 y)3=2 (25) where x is the first derivative with respect to x and xx is the second derivative with respect to x. The role of the curvature term is to control the regularity of the contour and  controls the balance between the regularity and robustness of the contour. Chan Vese formulated the energy function F in terms of an internal force Eint and an external force Eext F(C) = R 1 0 [Eint(C(S)) + Eext(C(S))]ds (26) Eint = length(C) + Area(Cin) (27) Eext = R Cin j I(x; y) à ´Ã‚€Â€Â€ I1 j2 + R Cout j I(x; y) à ´Ã‚€Â€Â€ I2 j2 (28) where  and  are positive fixed parameters which help to smoothen the growing contour. I(x; y) is intensity value of image region and I1 and I2 are average intensity value inside and outside the object region, respectively. IV. IMPLEMENTATION AND ANALYSIS All qualitative and quantitative outcome of the algorithm were recorded by running the Matlab programs with Intel(R) Core (TM) i7 CPU, 3.4 GHz, 4 GB RAM with Matlab 14 (a) on Windows 8. A. Description of Test Data The dataset used in the proposed algorithm consists of scanned images of stained breast biopsy slides from MITOS dataset [35]. Each set is composed of 96 high power field (HPF) images of breast tissue scanned at 40X magnification using two different scanners, Aperio (AP) and Hamamatsu (HM), with a resolution of 0.23-0.24 m:. All the images are 1376  1539  3 size. B. Experimental Strategies This paper qualitatively and quantitatively compares the KHO based optimal nuclei detection performance with the watershed based detection done by S. Ali et al. [8] and blue ratio image based detection done by Irshad et al. [21]. The segmentation performance is compared with local threshold method done by Cheng Lu et al. [22]. 1) Experiment 1: Evaluating the optimal threshold value: Goal of this experiment was to prove the power of KHO based optimal thresholding to detect the exact nuclei regions in histology images. It also compares the optimum value of the threshold obtained by KHO in breast histopathology images with GA, HSA and BFA. 2) Experiment 2: Comparison of Detection Accuracy: Aim of this work is to validate the detection performance of the proposed technique against the watershed and blue ratio techniques in terms of detection sensitivity and precision. 3) Experiment 3: Comparison of Segmentation Accuracy: This evaluates the performance of the detection algorithm in ACM segmentation and compare the results against two state-of-the-art techniques in terms of boundary based distance measures. This experiment also measure the strength of the algorithm to resolve the touching nuclei in terms of touching nuclei resolution.1) Evaluation of Detection Performance: This paper qualitatively and quantitatively evaluates the application of optimal thresholding in nuclei detection performance. The mean objective value and standard deviation express the consistency and stability of the algorithms. The results obtained by KHO are compared with GA, HSA and BFA. The parameters used in these algorithms are given in Table II.The quantitative evaluation of detection performance is carried out by locating the centroid of detected nuclear regions. The measures used to assess the nuclei detection comprise of: 1) Sensitivity (SD); 2) Positive Predictive value or Precision (PD); and 3) F-measure (FD) as given in eq. (26), (27), and (28), respectively. The results obtained are compared with manual detection results by an expert pathologist. The SD and PD values are computed from the number of truepositives (number of correctly detected nuclei, Ntp) , falsepositives (number of wrongly identified nuclei, Nfp) and false negatives(number of nuclei not detected by the algorithm, Nfn). The detected object is considered as true positive if its centroid is within 10 pixels range of manually determined centroid location. If no centroid was manually located within

The Super Continent Cycle Essay Example | Topics and Well Written Essays - 1000 words

The Super Continent Cycle - Essay Example This has been made possible by plate tectonics, the system driving Earth's continents slowly around the globe. Plate tectonics is the study of the movement of the huge plates of the landmass beneath the earth surface which results into drifting of the continents. This hypothesis of drifting continents was proposed by German scientist Alfred Wegener for the first time in 1912. He used many types of evidence available in abundance on the earth's surface. Some of the evidences pointing out such supercontinent cycle are; Fossil Remains: Similar types of plant and animal fossils were found in different areas of continents which were studied to be connected. For example, the fossil remains of a small reptile found both in Africa and Latin America. Rock Formations: In the coastal regions, the rocks were found to be matching even in areas which were widely separated. To prove this point Wegener came out with the proof suggesting the reconstruction of an ice cap radiating from South Africa, whose marks were traced across the southern continents. Climatic Conditions: Some climatic patterns were observed which were not in conformity with the normal climate of the region/s, thus suggesting that these climatic conditions could have been affected by the climatic conditions at some other places or regions. Wegener's hypothesis therefore led us to believe that while on the one hand the some of the western African regions have similarities with the eastern part of South America; the northern part of African continent had similarities with the southern regions of North America. Similarities were also found in the southern part of Asian region and the western part of African continent, thus giving the thought an impetus. Initially though Wegener's hypothesis was not taken seriously, but gradually, as the theory of plate tectonics developed in 1960's, more and more studies took place, the notions of supercontinent gained wider acceptance. The plate tectonics theory believes that the surface of earth is divided into a number of shifting plates with an average thickness of around 50-80 km. African, American, Antarctic, Eurasian, Indian and Pacific regions have all been assigned huge plates while smaller landmasses with smaller plates are identified as Arabian, Caribbean, Cocos, Nasca, Philipp ine and Scotia regions. In fact scientists have identified about 15 major tectonic plates. Earthquakes help in identifying the plates. The supercontinent theory suggests that during the Paleozoic Era, there was a huge continent named Pangeae, which included all the continents. The name Pangaea is derived from the Greek word "pan" meaning "all" and Gaea or Gaia i.e. the Greek name of the divine personification of the Earth. Pangaea, therefore, means "all land." During the Triassic Period, the Pangeae started fragmenting thus resulting in the existing number of continents. This process is said to be continuing even now. The supercontinent theory suggests such occurrences have also happened in the past, thus the name 'supercontinent cycle'. Canadian geologist John Tuzo Wilson also provided an insight into the hypothetical supercontinent cycle, who described the fragmentation of continents, opening and closing of the ocean basin and subsequent reassembly of the continents. This theory suggests t

Corporate Strategy - Analysis of Michael Porter Essay

Corporate Strategy - Analysis of Michael Porter - Essay Example Companies were not willing to take risks and venture into path that was not trodden earlier by some one else. In the information technology sector, imitation became inevitable as emerging economies allowed inwards flow of FDI. When multinationals started expanding to low cost countries they had to enter in joint venture with a local partner, which means they had to transfer technology. When firms entered India, they had to opt for joint ventures. While older technologies are transferred through licensing agreement, new technologies or those with fewer previous transfers or where the transferors have little experience with technology transfers opt for FDI (Eapen & Hennart, 2002). Porter further says, in high-tech industries this imitation phase often continues much longer than it should. This is because once the companies become established they do not plan for anything new and do not have any clear strategic. Stagnation occurs, which results in mediocre returns. Companies that come out with fundamental advantages prosper such as Toyota in the automobile sector. The Big Three in the US automotive industry namely, Ford Motor Company (Ford), General Motors Corporation (GM) and DaimlerChrysler (DC) played a prominent role in the evolution of the automotive industry till the 1990s. The industry adopted the lean production technique from Japan in the 1990s. The auto industry is the most globalized in the world and has undergone turbulent changes. The industry has been facing issues such as facing issues such as slow time to market, costly inventories, overcapacity, and low customer satisfaction and loyalty (Deloitte, 2003). The Big Three did not take initiatives to bring about fundamental changes as technology evolved. This allowed others such as Toyota and Hyundai to dominate the world market. Today Toyota is America’s third most admired organization and enjoy a 17.4 percent share of the US retail market (SD, 2007). Toyota has