A grayscale image can be viewed as a topological surface and this way, objects of interests may appear as peaks (sharp mountains), domes (smooth hills) or valleys (V- or U-shaped). Generally, the dome top presents more than one local maximum. Thus, it can be characterized by a local maximum cluster. Segmenting objects individually in images where they appear partially or totally fused is a problem which frequently may not be solved by a watershed segmentation or a basic morphological processing of images. Other issue is counting similar objects in images segmented beforehand. Counting them manually is a tedious and time-consuming task, and its subjective nature can lead to a wide variation in the results. This work presents a new method for segmenting and counting of local maximum clusters in digital images through a graph-based approach. Using the luminance information, the image is represented by a region adjacency graph and a graph-mining algorithm is applied to segment the clusters. Finally, according to image characteristics, a graph-clustering algorithm can be added to the process to improve the final result. The object counting step is a direct result from the mining algorithm and the clustering algorithm, when the latter is applied. The proposed method is tolerant to variations in object size and shape and can easily be parameterized to handle different image groups resulting from distinct objects. Tests made on a database with 262 images, composed of photographs of objects (group 1) and embryonic stem cells under fluorescence microscopy images (group 2), attest the effectiveness and quality of the proposed method as for segmentation and counting purpose. The images form group 1 processed by our method were checked by the author and those ones from group 2 by the specialists from the Institute of Biomedical Sciences at UFRJ. For these images we obtained an average F-measure of 85.33% and 90.88%, respectively. Finally, a comparative study with the widely used watershed algorithm was done. The watershed achieved an average F-measure of 74.02% e 78.28% for groups 1 and 2, respectively, against 85.33% e 91.60% obtained by our method.