You can achieve this effect by giving the value both a default_value and an implicit_value.
The default_value will be used when the option is not specified at all. The implicit_value will be used when the option is specific without a value. If a value is specified, it will override the default and implicit.
So, some code to do this could look something like this:
#include "boost/program_options.hpp"
#include <iostream>
#include <string>
using namespace std;
int main(int argc, char** argv)
{
    namespace po = boost::program_options;
    po::options_description desc("Options");
    desc.add_options()
        ("process-jpeg,e", po::value<string>()->default_value("")->implicit_value("./"), "Processes a JPEG.");
    po::variables_map vm;
    try
    {
        po::store(po::parse_command_line(argc, argv, desc), vm);
        po::notify(vm);
    } catch (po::error& e) {
        cerr << "ERROR: " << e.what() << endl << endl << desc << endl;
        return 1;
    }
    string outputDir = vm["process-jpeg"].as<string>();
    if (outputDir.empty()) {
        cout << "-e was not provided on the command line" << endl;
    } else {
        cout << "-e is using directory: " << outputDir << endl;
    }
}
Running this example code prints:
$ ./jpg_processor
-e was not provided on the command line
$ ./jpg_processor -e
-e is using directory: ./
$ ./jpg_processor -e c:\tmp
-e is using directory: c:\tmp