The main focus of the study is to compare the different entropy measures using exponential and size biased moment exponential distribution. Three different types of entropies have been compared. These entropies are Residual & Past entropies, α order entropies and α,β order entropies. These entropies have been compared mathematically, numerically and graphically. The generalized α order entropies and α,β order entropies for exponential distribution and SBM exponential distribution derived in chapter 3. Residual & Past entropies also derived in this chapter for both distributions. A new entropy has been derived using the hazard rate of the distribution. New entropy (HN1) produced the same result as Shannon’s 1948 entropy produces. This entropy fulfills the additive property of the Shannon entropy. HN1 is an alternate of the Shannon’s entropy. By extending the idea of hazard rate function, three new α order entropies have been derived. These entropies HN2, HN3 and HN4 produces the results same as Renyi’s (1961) entropy, Havrda & Charvat (1967) and Tsallis (1988) entropies respectively. This indicates that hazard rate is an information function. Another generalized α, β order entropy A1 has been derived. This is more generalized form of the entropy. Renyi (1961), Sunoj & Linu (2010), Rao et al. (2004) and Shannon (1948) entropies are the special cases of A1 entropy for different values of α and β. Residual and past entropies also derived for both distributions and compared. There are two new residual entropies A2, A4 and one past entropy A3 has been derived. These three entropies are also in generalized form. Thiswill produce number of residual entropies and past entropies using different values of α, β. A numerical study has been conducted for the comparison. Awad & Alwaneh (1987) introduced relative loss for the comparison of entropies. In this study relative loss of all entropies have been derived and compared. The result of relative loss is negative for majority of α order entropies. This shows that entropy of SBME distribution is higher as compare to the exponential distribution except Awad et al. (1987) entropy measures. Awad et al. (1987) entropies show the positive result which implies that exponential distribution has higher entropy as compare to others. Residual & past entropy also shows the negative results of relative loss and indicates that SBME distribution has higher entropy as compared to others. Statistical interpretation of the entropy and relative loss is not so easy. Higher entropy of the distribution concludes that there is high randomness in the distribution. Graphical trend of the entropies shows the exponential decay for both distributions. The trend of new entropy A3 is exponentially increasing instead of the decreasing. The concluding remarks of the study is in favor of the new entropies. As new entropies produced the results same as old entropy measures. There are some important characteristics of the new entropies. In the hazard rate, denominator will have replaced another probability density function or distribution function, this will produce the comparison method of entropies. When the hazard rate replaced with the conditional probability density function, this is another comparison method for entropies. The derivation of new entropies is difficult if the hazard rate has complicated expression.
Islam has provided guidance in agriculture like any other field of life. Agriculture provides food and nourishment to men, animals and birds. Pakistan is an agricultural land. Out of total grass root of Pakistan economy, 80% depends upon the agriculture. Agriculture is the production of food, feed and fiber by the systematic harvesting of plants and animals. The history of agriculture is a central element of human history. The article deals with the study of Muslims’ contribution to agriculture especially the Prophetic and four caliphs’ time. The Prophet r initiated the development of a sophisticated system of irrigation, and the Caliphs Hazrat Umar R. A and Hazrat Uthman R. A suggested revolution in agricultural reforms. The Islamic rules on land ownership and labor rights, alongside the recognition of private ownership and introduction of share cropping created by incentives to engage in agriculture. The present system prevailing in Pakistan has several short comings. Landlordism and poverty of cultivators who are generally uneducated, absence of heavy machinery for cultivation and small holdings also create problem.
Visual object tracking is an active and challenging computer vision research domain having wide range of civil and defence applications. Mean shift (MS) is a commonly used target tracking technique due to its ease of implementation and real time response. However, it has certain short-comings that limits its tracking performance. In this thesis short comings of MS tracking like poor localization, complicated background distraction, partial/ full occlusion and distraction due to similar target resemblance are addressed using 2D and 3D features. To improve MS target localization problem due to the presence of complex/mingled background features (in target representation), a novel 2D spatio-spectral technique is proposed. True background weighted histogram features are identified in target model representation using spectral and spatial weighting. A transformation is then applied to minimize their effect in target model representation for localization improvement. Edge based centroid re-positioning is applied to adjust/re-position the MS estimated target position for further localization improvement. Occlusion avoidance method is developed for MS tracking algorithm using adaptive window normalized cross correlation (NCC) based template matching. The Bhattacharyya coefficient based similarity threshold is used to detect partial/full occlusion and to initiate the NCC part in MS tracking. A target model updation for background weighted histogram through online feature consistency data is also proposed. The proposed 2D MS tracking techniques effectively solved the tracking problems of clutter, similar target resemblance, complex/fast object movement and partial/ full occlusion. The failure cases for proposed 2D tracking technique include guidewire tip tracking for image guided cardiovascular interventions. The guidewire tip being thin, featureless and deformable structure is easily distracted with its own and similar object like vane iii structures in neighborhood. Moreover, the tracking of guidewire under low contrast fluoroscopic images and abrupt shape variations due to cardiac motion make the problem more challenging. 3D visual tracking techniques are used to incorporate object depth information to improve robustness. However, the existing 3D tracking techniques lack accuracy and robustness mainly due to non availability of precise depth features. In this thesis, depth features are acquired through shape from focus (SFF) technique and integrated with spectral and spatial features for robust 3D target representation/tracking. For 3D shape representation through SFF, a novel adaptive focus measure based on linear combination of multiple morphological gradient operators is proposed. The morphological edge gradient operators aided by multi-structuring elements are employed for sharpness measurement. The robust focus measure is then computed by combining the weighted response of gradient operators. The depth features acquired are integrated in joint histogram with grey level intensity and texture features to develop a novel technique for real time 3D representation and tracking of guidewire for image guided cardiovascular interventions. The grey level intensity is represented through conventional histogram method whereas the texture and depth features are represented through filtered local binary pattern histogram and filtered local depth pattern histogram respectively. The result shows the significant improvement in the accuracy, robustness and computational efficiency through proposed 2D/3D MS tracking and depth estimation techniques.