|A better understanding of inter-dependency of various sunspot parameters such as magnetic field, intensity, temperature, size etc., and also their variation with strength of solar activity cycle is important to understand the magneto-convection process involved in sunspot formation and evolution and hence to develop a consistent sunspot model. We have investigated global sunspot properties using parameters of sunspots identified from stray-light-corrected continuum images from SoHO/MDI spanning from years 1996 to 2011. We find that the non-linear relation between umbral core intensity and sunspot size is best represented by an exponential function, which reaches an asymptotic value at 600MSH. For the first time we have also observed that the core intensity depends on shape of umbrae, i.e., circular umbrae are darker compared to the elongated ones. The core intensity also shows small variation with limb position; it increases slightly towards the limb. From our sunspots sampled from the complete solar cycle 23 and the rising phase of cycle 24, we did not find any solar-cycle variation in umbral core intensity. The penumbra to umbra area ratio shows slight dependence on sunspot size i.e., larger sunspots have relatively higher ratios. Leading and following sunspots usually have different morphological features, however in this study we did not observe significant differences in their core intensity and penumbra-umbra area ratio relation with sunspot area.