Automated registration of multiple mammograms for CAD depends on accurate nipple identification. We developed two new image analysis techniques based on geometric and texture convergence analyses to improve the performance of our previously developed nipple identification method. A gradient-based algorithm is used to automatically track the breast boundary. The nipple search region along the boundary is then defined by geometric convergence analysis of the breast shape. Three nipple candidates are identified by detecting the changes along the gray level profiles inside and outside the boundary and the changes in the boundary direction. A texture orientation-field analysis method is developed to estimate the fourth nipple candidate based on the convergence of the tissue texture pattern towards the nipple. The final nipple location is determined from the four nipple candidates by a confidence analysis. Our training and test data sets consisted of 419 and 368 randomly selected mammograms, respectively. The nipple location identified on each image by an experienced radiologist was used as the ground truth. For 118 of the training and 70 of the test images, the radiologist could not positively identify the nipple, but provided an estimate of its location. These were referred to as invisible nipple images. In the training data set, 89.37% (269/301) of the visible nipples and 81.36% (96/118) of the invisible nipples could be detected within 1 cm of the truth. In the test data set, 92.28% (275/298) of the visible nipples and 67.14% (47/70) of the invisible nipples were identified within 1 cm of the truth. In comparison, our previous nipple identification method without using the two convergence analysis techniques detected 82.39% (248/301), 77.12% (91/118), 89.93% (268/298) and 54.29% (38/70) of the nipples within 1 cm of the truth for the visible and invisible nipples in the training and test sets, respectively. The results indicate that the nipple on mammograms can be detected accurately. This will be an important step towards automatic multiple image analysis for CAD techniques.