This paper presents a new approach for the effective representation and classification of images of histopathological colon tissues stained with hematoxylin and eosin. In this approach, we propose to decompose a tissue image into its histological components and introduce a set of new texture descriptors, which we call local object patterns, on these components to model their composition within a tissue. We define these descriptors using the idea of local binary patterns, which quantify a pixel by constructing a binary string based on relative intensities of its neighbors. However, as opposed to pixel-level local binary patterns, we define our local object pattern descriptors at the component level to quantify a component. To this end, we specify neighborhoods with different locality ranges and encode spatial arrangements of the components within the specified local neighborhoods by generating strings. We then extract our texture descriptors from these strings to characterize histological components and construct the bag-of-words representation of an image from the characterized components. Working on microscopic images of colon tissues, our experiments reveal that the use of these component-level texture descriptors results in higher classification accuracies than the previous textural approaches.