## 1 Introduction  
Since forests are important for human life, forest inventories have been investigated for various purposes for centuries. In Europe, the first inventories were carried out in the 14 th and 15 th century for the purpose of intensive mine development. Since the 1910s, national forest inventories have been carried out in Norway, Sweden, and Finland, with an emphasis on timber production [1]. However, the demands of society have changed rapidly over recent decades. In this context, the principles for the conservation and sustainable management of forests have been newly added by the United Nations General Assembly [2]. This was in response to an increasing interest in non-timber aspects of forest structure and the demand for assessing these aspects [3]. In the Republic of Korea, in the 1970s, when the forest inventory was first investigated, it was aimed at reforestation and forest statistics. The purpose of the forest inventory has changed as the value of forest resources and impacts on the environment have evolved. Currently, forest inventories are developed to provide information that is useful to achieve the following goals: to maintain a healthy forest ecosystem, to preserve and protect the global environment and to promote sustainable development [4; 5; 6]. The vertical structure of a forest, which generally has four layers, is one of several elements representing forest vitality. In temperate zones, the forests are divided into layers of canopy, understory, shrub, and grass. The ability of the lower vegetation layer to grow under the canopy layer is determined by the condition of the soil, the species of vegetation, and the quantity of sunlight received by the lower vegetation layer due to the opening and closing rate of the crown [7; 8; 9]. In the case of artificial forests, they are usually single- or double-layered forests, as they are planned and managed for the purposes of wood production and agriculture. Natural forests however, have formed from a variety of vegetation communities through natural succession over lengthy periods of time, and have multiple layers. From an ecological point of view, natural forests with multiple-layers are highly resistant to pests, diseases, and environmental stress, and have high quality ecosystem services, such as providing habitats for wildlife. This is not the case with single-layered forests [10; 11; 12; 13; 14]. Therefore, vertical structure is a useful measure to evaluate the environmental aspects of a forest. Typically, forest inventories have been investigated through terrestrial surveys. The Korea Forest Service currently uses aerial orthophotos to survey forests, but it is very difficult to understand forest structure because orthophotos only image the forest canopy. Thus, a field survey is required to understand the stratification of a forest. In Korea, more than 70% of the country is made up of mountainous areas, and a nationwide field survey would be very time- and cost-consuming. Since remote sensing data is advantageous for extensive regional studies [15], we attempt to develop a method of effective forest inventory using remotely sensed data. Such a method could reduce the time and cost of a forest inventory. Multi-layered mature forests normally have a rough texture in remotely-sensed images, while single-layered young forests have a smoother texture [16; 17; 18]. Therefore, the structure of a forest can be estimated through the reflectance differences among the communities. The arrangement of the crown layer (canopy layer) in single-layered artificial forests can be considered consistent, but in natural forests it is inconsistent [17; 18]. Since tree height is closely related to forest vertical structure, lidar data used for tree height measurements can be used to classify a forest's vertical structure [7; 19; 20; 21; 22; 23; 24]. Lidar is an abbreviation for light detection and ranging, and is a device that measures the distance of a target using laser light.