http://www.h-o.nl/blog/using_category_images_in_your_magento_navigation/

Category.php

     public function getThumbnailUrl()
     {
         $url = false;
         if ($image = $this->getThumbnail()) {
             $url = Mage::getBaseUrl('media').'catalog/category/'.$image;
         }
         return $url;
     }

Navigation.php

     public function getImageUrl($category)
     {
         return Mage::getModel('catalog/category')->load($category->getId())->getImageUrl();
     }
     
     public function getThumbnailUrl($category)
     {
         return Mage::getModel('catalog/category')->load($category->getId())->getThumbnailUrl();
     }

Navigation2.php

     public function drawItem($category, $level = 0, $last = false, $rendermode)
     {
         return $this->_renderCategoryMenuItemHtml($category, $level, $last, null, null, null, null, null, $rendermode);
     }

Navigation3.php

     protected function _renderCategoryMenuItemHtml($category, $level = 0, $isLast = false, $isFirst = false,
         $isOutermost = false, $outermostItemClass = '', $childrenWrapClass = '', $noEventAttributes = false, $rendermode)

Navigation4.php

        if($rendermode == 'image' && $this->getImageUrl($category)){
         	$html[] = '<img src="'.$this->getImageUrl($category).'" />';
         }else if($rendermode == 'thumbnail' && $this->getThumbnailUrl($category)){
         	$html[] = '<img src="'.$this->getThumbnailUrl($category).'" />';
         }

top.phtml

<li class="level-top"><a class="level-top" href="#"><?php echo $this->__('Your parent'); ?></a>
		<ul class="level0">
		<?php foreach ($this->getStoreCategories() as $_category):?>
		<?php 
		if ($_category->getId() == '3') { 
		    if (Mage::helper('catalog/category_flat')->isEnabled()) {
		        $children = (array)$_category->getChildrenNodes();
		        $childrenCount = count($children);
		    } else {
		        $children = $_category->getChildren();
		        $childrenCount = $children->count();
		    }
			if ( $childrenCount ) {
				$this_id = $_category->getId();
				foreach ( $children as $child ) {
					echo $this->drawItem($child); 
	          	}
			}
		} 
		?>
		<?php endforeach ?>
        </ul>
 </li>

top2.phtml

     echo $this->drawItem($child, 0, true,'thumbnail'); 

This solution is part of our blog post: Using category images in your Magento navigation. Please subscribe to our RSS or follow us on Twitter for tips & tricks, free Magento extensions and more.